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- W1997809309 abstract "A clique of a graph G is a complete subgraph maximal under inclusion and having at least two vertices. A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G. The clique-transversal number, denoted by τc(G), is the cardinality of a minimum clique-transversal set in G. Wang et al. (2014) proved that τc(G)=⌈n3⌉ for any 2-connected {K1,3,K4}-free 4-regular graph of order n, and conjectured that τc(G)≤10n+327 for a connected {K1,3,K4}-free 4-regular graph of order n. In this paper, we give a short proof of the aforementioned theorem of Wang et al. and show that the above conjecture is true, apart from only three exceptions." @default.
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- W1997809309 date "2015-07-01" @default.
- W1997809309 modified "2023-09-23" @default.
- W1997809309 title "The clique-transversal number of a <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si6.gif display=inline overflow=scroll><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>}</mml:mo></mml:mrow></mml:math>-free 4-regular graph" @default.
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- W1997809309 doi "https://doi.org/10.1016/j.disc.2015.01.039" @default.
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