4-coloring ($P_6$, bull)-free graphs
Fr\'ed\'eric Maffray, Lucas Pastor

TL;DR
This paper introduces polynomial-time algorithms for 4-coloring ($P_6$, bull)-free graphs and extends to k-coloring in ($P_6$, bull, gem)-free graphs, advancing graph coloring theory for specific graph classes.
Contribution
It provides the first polynomial-time algorithms for 4-coloring ($P_6$, bull)-free graphs and generalizes to k-coloring in ($P_6$, bull, gem)-free graphs.
Findings
Polynomial-time 4-coloring algorithm for ($P_6$, bull)-free graphs
Polynomial-time k-coloring algorithm for ($P_6$, bull, gem)-free graphs
Extension of coloring algorithms to broader graph classes
Abstract
We present a polynomial-time algorithm that determines whether a graph that contains no induced path on six vertices and no bull (the graph with vertices a, b, c, d, e and edges ab, bc, cd, be, ce) is 4-colorable. We also show that for any fixed k the k-coloring problem can be solved in polynomial time in the class of (, bull, gem)-free graphs.
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
