Combinatorics Seminar

Alexander Gavrilyuk
University of Memphis

On the non-existence of some Moore Cayley digraphs
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Shunzhe Zhang
University of Mississippi

Chords of longest cycles passing through a specified small set
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Chris Wells
Auburn University

Phase transitions in isoperimetric problems
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Xiangqian Zhou
Wright State University

The Strong Edge-Coloring of Graphs
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Dheer Noal Desai
University of Memphis

A general theorem in spectral extremal graph theory
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Robert Simon
London School of Economics and Political Science

Paradoxical Decompositions and Colouring Rules
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Songling Shan
Auburn University

An Ore-type condition for hamiltonicity in tough graphs and the extremal examples
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Sarah Allred
University of South Alabama

Vertex Contraction-Deletion Minors
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Guantao Chen
Georgia State University

On the coequal values of total chromatic number and chromatic index
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Kevin Grace
University of South Alabama

Some generalizations of the class of spikes
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Vaidyanathan Sivaraman
Mississippi State University

Hereditary Nordhaus-Gaddum graphs
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Lei Zhong
University of Mississippi

Saturation Numbers of Double Stars
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Kanchana Gamladdalage
University of Mississippi

The Independent Bondage Number of Planar Graphs with Degree Conditions and Girth Conditions (pdf)

Maarten De Boeck
University of Memphis

Neumaier graphs (pdf)

John Griesmer
Colorado School of Mines

Chromatic Number and Independence Number of Cayley Graphs on Abelian Groups (pdf)

Vaidyanathan Sivaraman
Mississippi State University

Forbidden induced subgraphs for threshold-like graph classes (pdf)

Guantao Chen
Georgia State University

The Goldberg-Seymour Conjecture (pdf)

Zixia Song
University of Central Florida

Multicolor Gallai-Ramsey Numbers of Cycles and Paths (pdf)

Jinko Kanno

Quasi-surfaces: Chromatic Numbers and Euler’s Formula (pdf)

Haiying Wang
China University of Geosciences, Beijing

New Results on the Integral Sum Graphs (pdf)

Xuezheng Lv
Renmin University of China

r-hued chromatic number of P_t-free graphs (pdf)

Huiqing Liu
Hubei University, China

On the signless Laplacian eigenvalues related to independence number of graphs (pdf)

Mark Ellingham
Vanderbilt University

Quadrilateral embeddings of cartesian product graphs (pdf)

Yongtang Shi
Nankai University

Some Extremal Problems of Graphs and Hypergraphs (pdf)

David Grynkiewicz
University of Memphis

A Zero-Sum Conjecture of Hamidoune (pdf)

Chengfu Qin
Guangxi Normal University, China

The chain theorem of 4-connected graphs (pdf)

Ron Gould
Emory University

On Chorded Cycles (pdf)

Xiaoya Zha
Middle Tennessee State University

Thickness and outerthickness of graphs embedded in surfaces (pdf)

Suil O
Simon Fraser University

Fractional matchings of graphs (pdf)

Russ Woodroofe
Mississippi State University

Unimodal f-vectors and h-vectors of trees (pdf)

Thai Hoang Le
University of Mississippi

Additive bases in groups (pdf)

Feng Wang
University of Mississippi, Department of Computer Science

On Reliable Broadcast in Low Duty-Cycle Wireless Sensor Networks (pdf)

Xiangqian Zhou
Wright State University

Fundamental Graphs for Binary Matroids (pdf)

Aimei Yu
Beijing Jiaotong University

Hamiltonian-Connected Line Graphs with Given Degree Sums (pdf)

Ted Dobson
Mississippi State University and University of Primorska

Automorphism groups of codes (pdf)

Paul Balister
University of Memphis

Subtending many angles with few points (pdf)

Hong-Jian Lai
West Virginia University

Eigenvalues and Spanning Tree Packing of Graphs (pdf)

William Staton
University of Mississippi

Moore Graphs of Diameter two: The Homan-Singleton Problem (pdf)

Hehui Wu
University of Mississippi

Fractional Chromatic Number of Random Subgraphs (pdf)

James Reid
University of Mississippi

Clones in Matroids (pdf)

Jie Ma
Carnegie Mellon University/USTC

Digraph Coloring and Forbidden Cycle (pdf)

Richard Johnson
University of Memphis

The Robber Locating Game (pdf)

Tomas Juskevicius
University of Memphis

On a conjecture of Leader and Radcliffe related to the Littlewood-Offord problem (pdf)

Dominik Vu
University of Memphis

Combinatorial search and separating families (pdf)

Tomas Juskevicius
University of Memphis

On a conjecture of Leader and Radcliffe related to the Littlewood-Offord problem (pdf)

Dong Ye
Middle Tennessee State University

Decomposing cubic graphs with low genus (pdf)
It was conjectured by Ho man-Ostenhof that the edge set of every cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. We prove the conjecture for 3-connected cubic graphs with low genus. Our method provides a polynomial time algorithm to nd the decomposition.

Vladimir Nikiforov
University of Memphis

Some analytic methods for hypergraphs (pdf)
This talk will present an analytic approach for studying hypergraphs. The roots of the method are in the spectral theory for 2-graphs and in the theory of variational spectra of hypermatrices. The basic concepts of the method give a single viewpoint to a number of problems in hypergraphs, erasing the dierences between spectral and nonspectral results. The approach is particularly appropriate for extremal problems; for example it allows to prove that spectral extremal problems for hypergraphs are asymptotically equivalent to the corresponding edge extremal problems. This talk is not too technical and it should be interesting for a wider audience.

James Reid
University of Mississippi

The Matroids Without a Small Minor (pdf)
This talk includes an introduction to Matroid Theory, an exposition of classical results on graph minors, and extensions of these results from graphs to matroids. Joint work with Kayla Harville and Haidong Wu is presented on excluded minors in the classes of regular and binary matroids. The proofs of these results are both theoretical and computer-based.

Haidong Wu
University of Mississippi

Characterizing 3-connected binary matroids with no P9-minor (pdf)
Kuratowski’s Theorem states that a graph is planar if any only if it has no minor that is isomorphic to K3,3 or K5. Mayhew, Royle and Whittle characterize internally 4-connected binary matroids with no M(K3,3)-minor. Oxley characterizes 3-connected binary matroids without any P9- or P∗9-minor. In this paper, we give a complete characterization of 3-connected binary matroids with no P9-minor. Such a matroid is either one of the non-regular minors of a special 16-element matroid Y16; a 3-connected regular matroid; a binary spike with rank at least four; or is a matroid in an infinite class of matroids called starfishes. This is joint work with Guoli Ding at LSU.

Hehui Wu
University of Mississippi

Triangle-free subgraph with high fractional chromatic number (pdf)
A classic theorem states that for any k and l, there exists a graph with girth at least l, and chromatic number at least k. In 1970’s, Erd˝os and Hajnal proposed a conjecture that for any k, l, there exists a number f(k,l), such that if G has chromatic number at least f(k,l), then it contains a subgraph with chromatic number at least k and girth at least l. In 1977, Rödl proved that it is true for l = 3, that is, if the chromatic number is sufficiently large enough, that it contains a triangle-free subgraph with large chromatic number. Recently, we proved an analogous result for fractional chromatic number: for any k, there exists a f(k), such that if the fractional chromatic number is at least f(k), then it contains a triangle-free subgraph with fractional chromatic number at least k. This is joint work with Professor Bojan Mohar at Simon Fraser University.

John Estes
Belhaven University

Hamiltonian cycles through a given edge of more than 1-tough chordal planar graphs (pdf)

Shaohui Wang
The University of Mississippi
Multiplicative Zagreb indices of k-trees (pdf)

Jinko Kanno
Louisiana Tech University

Genus and Other Graph Invariants (pdf)
The minimal non-embeddable graphs for the torus are unknown (numerous). It may be a good approach to break the toroidal graphs into tractable subclasses and nd obstructions or some characterizations for each subclass. Those subclasses can be: H-minor free toroidal graphs with a small graph H, or the classes having the same number for some graph invariants including non-orientable genus, thickness, outer-thickness, or possibly the essential curve number for toroidal graphs, which will be introduced in this talk.

Chris Rodger
Auburn University

Amalgamations and Hamilton Decompositions (pdf)

William Staton
University of Mississippi

k-Trees, k-Frames, Shells and Independence Polynomials (pdf)

Stan Dziobiak
University of Mississippi

On Excluded and Unavoidable Minors in Graphs (pdf)

James Shook
National Institute of Standards and Technology

Math at the National Institute of Standards and Technology (pdf)

Kayla Davis Harville
University of Mississippi

On Regular and Binary Matroids Without Small Minors (pdf)

Hehui Wu
McGill University, Canada

Nearly Tight Linear Programming Bounds for Demand Matching in Bipartite Graphs (pdf)

Jaromy Kuhl
University of West Florida

Complete tripartite graphs and their competition numbers (pdf)

Emlee Nicholson
Millsaps College

Degree sum condition for k-ordered hamiltonian connected graphs (pdf)

Wanda Payne
University of Mississippi

Well-covered k-trees, k-frames, and unique colorability (pdf)

Hehui Wu
McGill University, Canada

Longest Cycles in Graphs with Given Independence Number and Connectivity (pdf)

Stan Dziobiak
University of Mississippi

Using Mathematica for Graph Theoretical Computations (pdf)

James Shook
National Institute of Standards and Technology

Affiliation Networks (pdf)

Stan Dziobiak
University of Mississippi

3-Connected Graph of Path-Width at Most Three (pdf)

James Shook
University of Mississippi

On Finding a Minimum Toughness Condition for a k-Tree to be Hamiltonian (pdf)

Cameron Byrum
University of Mississippi

How Many Holes Can an Unbordered Partial Word Contain?

Zhiquan Hu
Central China Normal University

Linked Graph with Modular Constraints (pdf)

James Reid
University of Mississippi

On a class of matroid designs (pdf)

Bruce Priddy
University of Mississippi

Domination and Independent Domination in Graphs (pdf)

Guantao Chen
Georgia State University

Long Cycles in 3-Connected Graphs with Bounded Degrees (pdf)

Xuechao Li
University of Georgia

Lower Bounds of Edge Critical Graphs (pdf)

Manoel Lemos
Universidade Federal de Pernambuco, Brazil

On triangle-free 3-connected matroids (pdf)

Xiaojuan Li
Urumqi Vocational University, China

Some results on path-factors in graphs (pdf)

Michal Karonski
Adam Mickiewicz University, Poland

On the 1-2-3-conjecture (pdf)

Xiangqian Zhou
Wright State University

Clones in representable matroids over a finite field (pdf)

William Staton
University of Mississippi

On the shell of some graphs (pdf)

Sivan Altinakar
École Polytechnique, Montréal, Canada

On compact edge-colorings : a polynomial time reduction from k-linear to k-cyclic (pdf)

Hao Li
LRI, UMR8623 CNRS and Universite Paris-sud 11

Cycles and subsets of vertices in graphs (pdf)

James Reid
University of Mississippi

On minimally k-connected matroids (pdf)

Sandra Spiroff
University of Mississippi

A Comparison of Zero Divisor Graphs (pdf)

Carolyn Chun
Louisiana State University

A chain theorem for internally 4-connected matroids (pdf)

Deborah Chun
Louisiana State University

Deletion-Contraction Polynomials (pdf)

Xianqian Zhou
Wright State University

Signed Graphs and Their Matroids (pdf)

James Shook
University of Mississippi

A characterization of the Centers of Chordal Graphs (pdf)

James Reid
University of Mississippi

On Circuit Sizes of Binary Matroids (pdf)

Haidong Wu
University of Mississippi

Non-separating co-circuits in 3-connected binary matroids (pdf)

Lei Cao
University of Mississippi

Decoding of Huffman codes with self-synchronization strings (pdf)

James Reid
University of Mississippi

Recent Results on Clones in Matroids (pdf)

Hongjian Lai
West Virginia University

Every 6-connected line graph is hamiltonian (pdf)

R. H. Schelp
University of Memphis

Ramsey Unsaturated and Saturated Graphs (pdf)

James Reid
University of Mississippi

Clones in Representable Matroids (pdf)

Jakayla Robbins
University of Mississippi

Orienting the free spikes (pdf)

Haidong Wu
University of Mississippi

An introduction to the Tutte Polynomial (pdf)

Laura Sheppardson
University of Mississippi

Graph generations for predictive chemistry (pdf)

Manoel Lemos
Federal University of Pernambuco, Brazil

Triads in 3-connected Matroids (pdf)

Guantao Chen
Georgia State University

Plane Graphs with Positive Curvature (pdf)

James Reid
University of Mississippi

“Intersections” of Linearly Largest Circuits in Matroids (pdf)

Xueliang Li
Center for Combinatorics, Nankai University

Trees with Maximum General Randic Index (pdf)

Xingxing Yu
Georgia Institute of Technology

Bonds in 3-connected Mulitgraphs (pdf)

Klas Markström
Umea University

The Cycle Double Cover Conjecture II (pdf)

Klas Markström
Umea University

An Introduction to Cycle Double Cover Conjecture (pdf)

Bing Wei
University of Mississippi

Chords in Longest Cycles of Graphs (pdf)

Xiaoya Zha
Middle Tennessee State University

Closed 2-cell Embeddings of Graphs Embeddable in the Projective Plane and the Torus (pdf)

Xueliang Li
Center for Combinatorics, Nankai University

Recent Results and Problems in General Randic Index (pdf)

Josh Hanes
University of Mississippi

On Szemeredi’s Regularity Lemma (pdf)

Hongjian Lai
West Virginia University

Group connectivity of a graph (pdf)

Laura Sheppardson
University of Mississippi

Planar decomposition of graphs (pdf)

William Staton, Benton Tyler (pdf)
University of Mississippi

An Extremal Problem for Graphs with Large Odd Girth

James Reid
University of Mississippi

Job Assisgnment Problems (pdf)

Tristan Denley
University of Mississippi

The Bela Bash (pdf)

Bing Wei
University of Mississippi

Graph Minors and Linkages III (pdf)

Bing Wei
University of Mississippi

Graph Minors and Linkages II (pdf)

Bing Wei
University of Mississippi

Graph Minors and Linkages (pdf)

Bing Wei
University of Mississippi

On the total domination number of graphs (pdf)

Haidong Wu
University of Mississippi

Chords in Graphs (pdf)

William Staton
University of Mississippi

On the Bipartite Density of a Graph (pdf)

James Reid
University of Mississippi

On largest bond conjecture in graphs