Strong edge coloring of circle graphs. (May 2022)

• Record Type: Journal Article
• Authors: Dębski, Michał; Śleszyńska-Nowak, Małgorzata
• Is Part Of: European journal of combinatorics. Volume 102(2022)
• Publication Date: 2022-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2022.103507
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: A strong clique in a graph G is a set S of edges of G such that every two edges in S are either adjacent or joined by an edge of G . We say that G is a circle graph if vertices of G correspond to chords of a circle and G contains an edge u v if and only if chords corresponding to u and v intersect. We show that the maximum size of a strong clique in a circle graph with maximum degree Δ is at most 5 4 Δ 2 . This bound is tight for even Δ and correct up to a smaller order error term for odd Δ . This result supports a conjecture of Erdős and Nešetřil from 1985, which states that the strong chromatic index of a graph with maximum degree Δ is at most 5 4 Δ 2 . It also confirms a conjecture of Faudree, Gyárfás, Schelp and Tuza from 1990 for circle graphs.