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A Different Short Proof of Brooks’ Theorem

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Rabern L.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 3

633-634

Lovász gave a short proof of Brooks’ theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case.

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On graphs G for which both g and G̅ are claw-free

100%

Fujita S.

Discussiones Mathematicae Graph Theory

2005

tom 25

nr 3

267-272

Let G be a graph with |V(G)| ≥ 10. We prove that if both G and G̅ are claw-free, then min{Δ(G), Δ(G̅)} ≤ 2. As a generalization of this result in the case where |V(G)| is sufficiently large, we also prove that if both G and G̅ are $K_{1,t}$-free, then min{Δ(G),Δ(G̅)} ≤ r(t- 1,t)-1 where r(t-1,t) is the Ramsey number.

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2 Discussiones Mathematicae Graph Theory

1 Fujita S.

1 Rabern L.

1 2014

1 2005

Wyniki wyszukiwania

A Different Short Proof of Brooks’ Theorem

On graphs G for which both g and G̅ are claw-free