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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
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18 papers · 2 filters
On the structure of (claw,bull)-free graphs
Sebastián González Hermosillo de la Maza, Yifan Jing, Masood Masjoody
In this research, we determine the structure of (claw, bull)-free graphs. We show that every connected (claw, bull)-free graph is either an expansion of a path, an expansion of a c…
A rainbow version of Mantel's Theorem
Ron Aharoni, Matt DeVos, Sebastián González Hermosillo de la Maza +2
Mantel's Theorem asserts that a simple vertex graph with more than edges has a triangle (three mutually adjacent vertices). Here we consider a rainbow variant…
Traversal with Enumeration of Geometric Graphs in Bounded Space
Sahand Khakabimamaghani, Masood Masjoody, Ladislav Stacho
In this paper, we provide an algorithm for traversing geometric graphs which visits all vertices, and reports every vertex and edge exactly once. To achieve this, we combine a give…
The structure of graphs with no K_{3,3} immersion
Matt DeVos, Mahdieh Malekian
The Kuratowski-Wagner Theorem asserts that a graph is planar if and only if it does not have either or as a minor. Using this Wagner obtained a precise description…
Constructing Geometric Graphs of Cop Number Three
Seyyed Aliasghar Hosseini, Masood Masjoody, Ladislav Stacho
The game of cops and robbers is a pursuit game on graphs where a set of agents, called the cops try to get to the same position of another agent, called the robber. Cops and robber…
Which graphs occur as -graphs?
Matt DeVos, Adam Dyck, Jonathan Jedwab +1
The -graph of a graph is the graph whose vertices are labelled by the minimum dominating sets of , in which two vertices are adjacent when their corresponding minimum dom…
Triangle-free subgraphs with large fractional chromatic number
Bojan Mohar, Hehui Wu
It is well known that for any integers and , there is a graph with chromatic number at least and girth at least . In 1960's, Erdős and Hajnal conjectured that for any…
A golden ratio inequality for vertex degrees of graphs
Fiachra Knox, Bojan Mohar, David R. Wood
Motivated by the study of the crossing number of graphs, it is shown that, for trees, the sum of the products of the degrees of the end-vertices of all edges has an upper bound in…
Fractional chromatic number of a random subgraph
Bojan Mohar, Hehui Wu
It is well known that a random subgraph of the complete graph has chromatic number w.h.p. Boris Bukh asked whether the same holds for a random subgraph of any $…
On walks avoiding a quadrant
Kilian Raschel, Amélie Trotignon
Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly relate…
The Algebraic Connectivity of a Graph and its Complement
B. Afshari, S. Akbari, M. J. Moghaddamzadeh +1
For a graph , let denote its second smallest Laplacian eigenvalue. It was conjectured that , where is the complement of $…
A new structure for difference matrices over abelian -groups
Koen van Greevenbroek, Jonathan Jedwab
A difference matrix over a group is a discrete structure that is intimately related to many other combinatorial designs, including mutually orthogonal Latin squares, orthogonal arr…
Short rainbow cycles in graphs and matroids
Matt DeVos, Matthew Drescher, Daryl Funk +5
Let be a simple -vertex graph and be a colouring of with colours, where each colour class has size at least . We prove that contains a rainbow cycl…
The Chromatic Number of Finite Group Cayley Tables
Luis Goddyn, Kevin Halasz, E. S. Mahmoodian
The chromatic number of a latin square , denoted , is the minimum number of partial transversals needed to cover all of its cells. It has been conjectured that every latin…
The genus of complete 3-uniform hypergraphs
Yifan Jing, Bojan Mohar
In 1968, Ringel and Youngs confirmed the last open case of the Heawood Conjecture by determining the genus of every complete graph . In this paper, we investigate the minimum…
3d positive lattice walks and spherical triangles
B Bogosel, V Perrollaz, K. Raschel +1
In this paper we explore the asymptotic enumeration of three-dimensional excursions confined to the positive octant. As shown in [29], both the exponential growth and the critical…
A counterexample to Las Vergnas' strong map conjecture on realizable oriented matroids
Pei Wu
The Las Vergnas' strong map conjecture, states that any strong map of oriented matroids can be factored into extensions and contractions.…
Structure and generation of crossing-critical graphs
Zdeněk Dvořák, Petr Hliněný, Bojan Mohar
We study -crossing-critical graphs, which are the minimal graphs that require at least edge-crossings when drawn in the plane. For there are only two such graphs witho…