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Finding a smallest odd hole in a claw-free graph using global structure
[article]
2011
arXiv
pre-print
A lemma of Fouquet implies that a claw-free graph contains an induced C_5, contains no odd hole, or is quasi-line. In this paper we use this result to give an improved shortest-odd-hole algorithm for claw-free graphs by exploiting the structural relationship between line graphs and quasi-line graphs suggested by Chudnovsky and Seymour's structure theorem for quasi-line graphs. Our approach involves reducing the problem to that of finding a shortest odd cycle of length ≥ 5 in a graph. Our
arXiv:1103.6222v2
fatcat:y4oa7m5f2fhuhkqqyknoiaumsi