6 papers
Yes, -free graphs are recolorable
Henry Echeverría, Owen Henderschedt
We prove that every -free graph is recolorable. Equivalently, for every such graph and every , the reconfiguration graph of proper -colorings…
On the recolorability of -free graphs
Henry Echeverría, Owen Henderschedt
Given a graph and an integer , the reconfiguration graph of the -colorings of has as its vertices as the proper -colorings of , with an edge betwe…
Coloring graphs with independence number two and no odd clique immersions
Henry Echeverría, Jessica McDonald
We study the chromatic number of graphs that exclude a clique as a strong odd immersion and have independence number two. Given a graph and , we prove that if…
Odd Hadwiger number and graph products
Henry Echeverría, Andrea Jiménez, Suchismita Mishra +2
The Odd Hadwiger number of a graph is the largest integer such that has a clique of size as an odd minor. In this paper, we investigate how large is the Odd Hadwige…
Totally odd subdivisions in Kneser graphs
Henry Echeverría, Andrea Jiménez, Suchismita Mishra +3
As evidence for the Odd Hadwiger Conjecture, Simonyi and Zsbán (2010) showed that every Kneser graph with large enough order (compared to ) contains a totally odd subdivi…
Totally odd immersions of complete graphs in graph products
Henry Echeverría, Andrea Jiménez, Suchismita Mishra +2
For a graph , let denote the maximum integer such that contains as an immersion. A recent paper of Collins, Heenehan, and McDonald (2023) studied the behav…