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Bipartite Powers of k-chordal Graphs

Chandran, Sunil L and Mathew, Rogers (2013) Bipartite Powers of k-chordal Graphs. In: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 15 (2). pp. 49-58. PDF dis_mat_the_com_sci_15-2_49_2013.pdf - Published Version Restricted to Registered users only Download (339kB) | Request a copy

Abstract

Let k be an integer and k >= 3. A graph G is k-chordal if G does not have an induced cycle of length greater than k. From the definition it is clear that 3-chordal graphs are precisely the class of chordal graphs. Duchet proved that, for every positive integer m, if G m is chordal then so is G(m+2). Brandst `` adt et al. in Andreas Brandsadt, Van Bang Le, and Thomas Szymczak. Duchet- type theorems for powers of HHD- free graphs. Discrete Mathematics, 177(1- 3): 9- 16, 1997.] showed that if G m is k - chordal, then so is G(m+2). Powering a bipartite graph does not preserve its bipartitedness. In order to preserve the bipartitedness of a bipartite graph while powering Chandran et al. introduced the notion of bipartite powering. This notion was introduced to aid their study of boxicity of chordal bipartite graphs. The m - th bipartite power G(m]) of a bipartite graph G is the bipartite graph obtained from G by adding edges (u; v) where d G (u; v) is odd and less than or equal to m. Note that G(m]) = G(m+1]) for each odd m. In this paper we show that, given a bipartite graph G, if G is k-chordal then so is G m], where k, m are positive integers with k >= 4

Item Type: Journal Article DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE, FRANCE k-chordal graph; hole; chordality; graph power; bipartite power Division of Electrical Sciences > Computer Science & Automation Id for Latest eprints 02 Jan 2014 06:27 02 Jan 2014 06:35 http://eprints.iisc.ac.in/id/eprint/48004 View Item