Coloring graphs with no induced five-vertex path or gem
M.Chudnovsky, T.Karthick, P.Maceli, Frederic Maffray

TL;DR
This paper provides a structural characterization of ($P_5$,gem)-free graphs and establishes a tight upper bound on their chromatic number relative to their clique number, advancing understanding in graph coloring.
Contribution
It offers an explicit structural description of ($P_5$,gem)-free graphs and proves a tight upper bound on their chromatic number based on clique number.
Findings
($P_5$,gem)-free graphs have a specific structure.
The chromatic number satisfies $oxed{ ext{chi}(G) \\le \\lceil rac{5 \\omega(G)}{4} ceil}$.
The bound is proven to be optimal.
Abstract
For a graph , let and respectively denote the chromatic number and clique number of . We give an explicit structural description of (,gem)-free graphs, and show that every such graph satisfies . Moreover, this bound is best possible.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
