output
19922026
most citedObservation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC

10.9k citations

Showing 2021 · math.COShow all

12 papers · 2 filters

math.CO2021

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…

math.CO2021

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…

math.CO2021

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…

math.CO2021★ 3 cited

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…

math.CO2021

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…

math.CO2021★ 1 cited

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…

math.CO2021★ 4 cited

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…

math.CO2021★ 2 cited

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…

math.CO2021★ 2 cited

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…

math.CO2021★ 3 cited

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…

math.CO2021★ 8 cited

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…

math.CO2021★ 4 cited

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)…