The fractional chromatic number binding functions of (cap, even hole)-free graphs

Chenglong Deng^* (corresponding author), Xuding Zhu

* Corresponding author: Chenglong Deng.

College Mathematics, Vol 1, Issue 1 (Winter 2026), pp. 13-20.

Open access. © 2026 the author(s). Published under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

This article belongs to an issue that is still in progress. Bibliographic details may change before formal publication in December, 2026.

Abstract

A hole is an induced cycle of length at least four, and a cap is a hole together with a vertex adjacent to exactly two consecutive vertices of the hole. We prove that if q2 and G is a (cap,even hole)-free graph with no odd hole of length at most 2q-1, then _f(G)2q+12q(G). The bound is best possible, as shown by clique blowups of C_2q+1.

How to cite

Chenglong Deng, Xuding Zhu. “The fractional chromatic number binding functions of (cap, even hole)-free graphs.” College Mathematics 1, no. 1 (2026): 13-20.