Geodesic
On the independence number of edge chromatic critical graphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 577-584

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In 1968, Vizing conjectured that for any edge chromatic critical graph G = (V,E) with maximum degree △ and independence number α(G), α(G) ≤ |V|/2. It is known that α(G) lt; 3∆−2/5∆−2|V|. In this paper we improve this bound when △≥4. Our precise result depends on the number n_2 of 2-vertices in G, but in particular we prove that α(G) ≤3∆−3/5∆−3|V| when △≥5 and n_2≤2(△− 1).
Keywords: edge coloring, edge-chromatic critical graphs, independence number 
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Pang, Shiyou; Miao, Lianying; Song, Wenyao; Miao, Zhengke. On the independence number of edge chromatic critical graphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 3, pp. 577-584. http://geodesic.mathdoc.fr/item/DMGT_2014_34_3_a9/