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12 papers · 2 filters
Single-conflict colorings of degenerate graphs
Peter Bradshaw, Tomáš Masařík
We consider the single-conflict coloring problem, a graph coloring problem in which each edge of a graph receives a forbidden ordered color pair. The task is to find a vertex color…
Proper orientations and proper chromatic number
Yaobin Chen, Bojan Mohar, Hehui Wu
The proper chromatic number $\Vecχ(G)$ of a graph is the minimum such that there exists an orientation of the edges of with all vertex-outdegrees at most and such t…
Cogrowth Series for Free Products of Finite Groups
Jason Bell, Haggai Liu, Marni Mishna
Given a finitely generated group with generating set , we study the cogrowth sequence, which is the number of words of length over the alphabet that are equal to one. Th…
Universality in minor-closed graph classes
Tony Huynh, Bojan Mohar, Robert Šámal +2
Stanislaw Ulam asked whether there exists a universal countable planar graph (that is, a countable planar graph that contains every countable planar graph as a subgraph). János Pac…
Multicoloured Ramsey numbers of the path of length four
Henry Liu, Bojan Mohar, Yongtang Shi
Let denote the path on vertices. The -coloured Ramsey number of , denoted by , is the minimum integer such that whenever the complete graph on v…
Integer decomposition property of polytopes
Sharon Robins
We study the integer decomposition property of lattice polytopes associated with the -dimensional smooth complete fans with at most rays. Using the classification of smoot…
On the hat guessing number of a planar graph class
Peter Bradshaw
The hat guessing number is a graph invariant based on a hat guessing game introduced by Winkler. Using a new vertex decomposition argument involving an edge density theorem of Erdő…
Tuza's Conjecture for Threshold Graphs
Marthe Bonamy, Łukasz Bożyk, Andrzej Grzesik +4
Tuza famously conjectured in 1981 that in a graph without k+1 edge-disjoint triangles, it suffices to delete at most 2k edges to obtain a triangle-free graph. The conjecture holds…
Robust Connectivity of Graphs on Surfaces
Peter Bradshaw, Tomáš Masařík, Jana Novotná +1
Let denote the set of leaves in a tree . One natural problem is to look for a spanning tree of a given graph such that is as large as possible. This proble…
Constant congestion brambles in directed graphs
Tomáš Masařík, Marcin Pilipczuk, Paweł Rzążewski +1
The Directed Grid Theorem, stating that there is a function such that a directed graphs of directed treewidth at least contains a directed grid of size at least as a…
Random 2-cell embeddings of multistars
Jesse Campion Loth, Kevin Halasz, Tomáš Masařík +2
Random 2-cell embeddings of a given graph are obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces, , of s…
The Phase Transition of Discrepancy in Random Hypergraphs
Calum MacRury, Tomáš Masařík, Leilani Pai +1
Motivated by the Beck-Fiala conjecture, we study the discrepancy problem in two related models of random hypergraphs on vertices and edges. In the first (edge-independent)…