James Davies

collaborators

3 papers

math.CO2026

On the chromatic number of the union of comparability graphs

Maria Chudnovsky, Wouter Cames van Batenburg, Linda Cook +3

Resolving in a strong sense a problem of GyÃ¡rfÃ¡s on the union of two perfect graphs, we prove that for every pair of positive integers $d$ and $k$ , there is a graph $G$ with cliq…

math.CO2026

Reuniting $I ¨ $ -boundedness with polynomial $I ¨ $ -boundedness

Maria Chudnovsky, Linda Cook, James Davies +1

A class $F$ of graphs is $I ¨ $ -bounded if there is a function $f$ such that $I ¨ (H) \leq f (I ¨ (H))$ for all induced subgraphs $H$ of a graph in $F$ . If $f$ can be ch…

math.CO2024

Geometric graphs with exponential chromatic number and arbitrary girth

Matija BuciÄ, James Davies

In 1975 ErdÅs initiated the study of the following very natural question. What can be said about the chromatic number of unit distance graphs in $R^{2}$ that have large gir…

On the chromatic number of the union of comparability graphs

Reuniting I¨-boundedness with polynomial I¨-boundedness

Geometric graphs with exponential chromatic number and arbitrary girth

Reuniting $I ¨ $ -boundedness with polynomial $I ¨ $ -boundedness