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Rank and biclique partitions of the complement of paths

✍ Scribed by Boyer, Elizabeth D.

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 230 KB
Volume: 27
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199803)27:3<111::aid-jgt1>3.0.co;2-r

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✦ Synopsis

The problem was posed of determining the biclique partition number of the complement of a Hamiltonian path (Monson, Rees, and Pullman, Bull. Inst. Combinatorics and Appl. 14 (1995), 17-86). We define the complement of a path P , denoted P , as the complement of P in K m,n where P is a subgraph of K m,n for some m and n. We give an exact formula for the biclique partition number of the complement of a path. In particular, we solve the problem posed in [9]. We also summarize our more general results on biclique partitions of the complement of forests.

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