On the chromatic index of graphs whose core has maximum degree two
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چکیده
Let G be a connected graph. The core of G, denoted by G∆, is the subgraph of G induced by the vertices of maximum degree. Hilton and Zhao [On the edge-colouring of graphs whose core has maximum degree two, JCMCC 21 (1996), 97-108] conjectured that, if ∆(G∆) ≤ 2, then G is Class 2 if and only if G is overfull, with the sole exception of the Petersen graph with one vertex deleted. In this paper we prove this conjecture for all graphs G of even order such that |V (G∆)| > max{ 1 2 |V (G)|, |V (G)| − 2∆(G) + 5}.
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تاریخ انتشار 2006