Crossing graphs of fiber-complemented graphs

• Published in: Discrete mathematics Vol. 308; no. 7; pp. 1176 - 1184
• Main Authors: Brešar, Boštjan, Horvat, Aleksandra Tepeh
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 06.04.2008; Elsevier
• Subjects: Applied sciences; Cartesian products; Computer science; control theory; systems; Exact sciences and technology; Expansion; Gated sets; Geometry; Information retrieval. Graph; Mathematics; Median graphs; Prefibers; Sciences and techniques of general use; Theoretical computing; 05C75; 05C12; Prefibers; Median graphs; Cartesian products; Expansion; Gated sets; Complete graph; Median graphs; Gated sets; Prefibers; Cartesian products; Expansion; Color; Chordal graph; Connected graph; Median; Parallelism; Product; Bipartite graph; 05C12;05C75; Cycle
• ISSN: 0012-365X; 1872-681X
• DOI: 10.1016/j.disc.2007.04.005

Fiber-complemented graphs form a vast non-bipartite generalization of median graphs. Using a certain natural coloring of edges, induced by parallelism relation between prefibers of a fiber-complemented graph, we introduce the crossing graph of a fiber-complemented graph G as the graph whose vertices are colors, and two colors are adjacent if they cross on some induced 4-cycle in G. We show that a fiber-complemented graph is 2-connected if and only if its crossing graph is connected. We characterize those fiber-complemented graphs whose crossing graph is complete, and also those whose crossing graph is chordal.