A proof of Hougardy's conjecture for diamond-free graphs
نویسندگان
چکیده
A pair of vertices of a graph is called an even pair if every chordless path between them has an even number of edges. A graph is minimally even pair free if it is not a clique, contains no even pair, but every proper induced subgraph either contains an even pair or is a clique. Hougardy (European J. Combin. 16 (1995) 17–21) conjectured that a minimally even pair free graph is either an odd cycle of length at least 8ve, the complement of an even or odd cycle of length at least 8ve, or the linegraph of a bipartite graph. A diamond is a graph obtained from a complete graph on four vertices by removing an edge. In this paper we verify Hougardy’s conjecture for diamond-free graphs by adapting the characterization of perfect diamond-free graphs given by Fonlupt and Zemirline (Maghreb Math. Rev. 1 (1992) 167–202). c © 2001 Elsevier Science B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 240 شماره
صفحات -
تاریخ انتشار 2001