Powers of cycles, powers of paths, and distance graphs

In 1988, Golumbic and Hammer characterized powers of cycles, relating them to circular-arc graphs. We extend their results and propose several further structural characterizations for both powers of cycles and powers of paths. The characterizations lead to linear-time recognition algorithms of these classes of graphs. Furthermore, as a generalization of powers of cycles, powers of paths, and even of the well-known circulant graphs, we consider distance graphs. While colourings of these graphs have been intensively studied, the recognition problem has been so far neglected. We propose polynomial-time recognition algorithms for these graphs under additional restrictions. Keywords. cycle; path; circulant graph; distance graph; circular arc graph; interval graph

• Type: Journal
• Year: 2011
• Where: DAM
• Authors: Min Chih Lin, Dieter Rautenbach, Francisco J. Soulignac, Jayme Luiz Szwarcfiter
• Keywords: Circulant Graph, DAM 2011, Distance Graph, Recognition Algorithms, Theoretical Computer Science