Mixed hypergraphs with bounded degree: edge-coloring of mixed multigraphs

An upper bound on the number of edges of

An upper bound on the number of edges of edge-coloring critical graphs with high maximum degree

✍ Lian-ying Miao; Shi-you Pang; Jian-liang Wu 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 100 KB

In this paper, we prove that any edge-coloring critical graph G with maximum degree ¿ (11 + √ 49 -24 )=2, where 6 1, has the size at least 3(|V (G)| -) + 1 if 6 7 or if ¿ 8 and |V (G)| ¿ 2 --4 -( + 6)=( -6), where is the minimum degree of G. It generalizes a result of Sanders and Zhao.