1 citations · 1 across the 13 of their papers we have counts for
7 papers · 1 filter
Improved Bounds for the Ultimate Independence Ratio of Odd Wheels
Alexander Clow, Hitesh Kumar, Shivaramakrishna Pragada
The ultimate independence ratio of a graph is defined as where is the independence…
A Note on Large Degenerate Induced Subgraphs in Sparse Graphs
Alexander Clow, Sean Kim, Ladislav Stacho
Given a graph and a non-negative integer let be the order of a largest induced -degenerate subgraph of . We prove that for any pair of non-negative integers…
Cops and Robbers on Graphs with Path Constraints
Alexander Clow, Erin Meger
In 2019, Sivaraman conjectured that every -free graph has cop number at most . In the same year, Liu proved this conjecture for -free graphs. Recently…
Tight Bounds for Cycle-Edge Decompositions and Covers
Saieed Akbari, Jonny Aloni, Arash Beikmohammadi +1
An old conjecture of Erd{ő}s and Gallai states that every vertex graph can be decomposed, that is can be partitioned, into cycles and edges. The covering version…
Cops and Robbers, Clique Covers, and Induced Cycles
Alexander Clow, Imed Zaguia
We consider the Cops and Robbers game played on finite simple graphs. In a graph , the number of cops required to capture a robber in the Cops and Robbers game is denoted by $c(…
On Gyárfás' Path-Colour Problem
Ben Cameron, Alexander Clow
In their 1997 paper titled ``Fruit Salad", Gyárfás posed the following conjecture: there exists a constant such that if each path of a graph spans a -colourable subgraph, th…
A Counterexample to a Conjecture of Lovász
Alexander Clow, Penny Haxell, Bojan Mohar
In 1975 Lovász conjectured that every -partite, -uniform hypergraph contains vertices whose deletion reduces the matching number. If true, this statement would imply a…