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- W1986957580 abstract "A hole of a graph is an induced cycle of length at least 4. Kim (2005) [2] conjectured that the competition number k ( G ) is bounded by h ( G ) + 1 for any graph G , where h ( G ) is the number of holes of G . In Lee et al. [3] , it is proved that the conjecture is true for a graph whose holes are mutually edge-disjoint. In Li et al. (2009) [4] , it is proved that the conjecture is true for a graph, all of whose holes are independent. In this paper, we prove that Kim’s conjecture is true for a graph G satisfying the following condition: for each hole C of G , there exists an edge which is contained only in C among all induced cycles of G ." @default.
- W1986957580 created "2016-06-24" @default.
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- W1986957580 date "2010-01-01" @default.
- W1986957580 modified "2023-09-29" @default.
- W1986957580 title "An upper bound for the competition numbers of graphs" @default.
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- W1986957580 doi "https://doi.org/10.1016/j.dam.2009.09.007" @default.
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