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On choosability of complete multipartite graphs $K_{4,3t,2(k-2t-2),1*(t+1)}$

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Zheng G.-P., Shen Y.-F., Chen Z.-L., Lv J.-F.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 2

237-244

A graph G is said to be chromatic-choosable if ch(G) = χ(G). Ohba has conjectured that every graph G with 2χ(G)+1 or fewer vertices is chromatic-choosable. It is clear that Ohba's conjecture is true if and only if it is true for complete multipartite graphs. In this paper we show that Ohba's conjecture is true for complete multipartite graphs $K_{4,3*t,2*(k-2t-2),1*(t+1)}$ for all integers t ≥ 1 and k ≥ 2t+2, that is, $ch(K_{4,3*t,2*(k-2t-2),1*(t+1)}) = k$, which extends the results $ch(K_{4,3,2*(k-4),1*2}) = k$ given by Shen et al. (Discrete Math. 308 (2008) 136-143), and $ch(K_{4,3*2,2*(k-6),1*3}) = k$ given by He et al. (Discrete Math. 308 (2008) 5871-5877).

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Chen Z.-L.

1 Lv J.-F.

1 Shen Y.-F.

1 Zheng G.-P.

1 2010

Wyniki wyszukiwania

On choosability of complete multipartite graphs $K_{4,3t,2(k-2t-2),1*(t+1)}$

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Chen Z.-L.

1 Lv J.-F.

1 Shen Y.-F.

1 Zheng G.-P.

1 2010

Wyniki wyszukiwania

On choosability of complete multipartite graphs $K_{4,3*t,2*(k-2t-2),1*(t+1)}$

On choosability of complete multipartite graphs $K_{4,3t,2(k-2t-2),1*(t+1)}$