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关于边着色临界图的一个问题
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作者 刘峙山 《内蒙古师范大学学报(自然科学汉文版)》 CAS 1991年第4期24-25,共2页
H.P.Yap在[1]中提出这样一个问题,是否存在偶阶边着色8临界图,它除了有一个2度点和两个3度点外其余的都是8度点?作为本文定理推论的一个特殊情形给出了这个问题的否定性答案。
关键词 连着色 临界图
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Graphs with vertex rainbow connection number two
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作者 LU ZaiPing MA YingBin 《Science China Mathematics》 SCIE CSCD 2015年第8期1803-1810,共8页
An edge colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of colors... An edge colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. A vertex colored graph G is vertex rainbow connected if any two vertices are connected by a path whose internal vertices have distinct colors. The vertex rainbow connection number of G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G vertex rainbow connected. In 2011, Kemnitz and Schiermeyer considered graphs with rc(G) = 2.We investigate graphs with rvc(G) = 2. First, we prove that rvc(G) 2 if |E(G)|≥n-22 + 2, and the bound is sharp. Denote by s(n, 2) the minimum number such that, for each graph G of order n, we have rvc(G) 2provided |E(G)|≥s(n, 2). It is proved that s(n, 2) = n-22 + 2. Next, we characterize the vertex rainbow connection numbers of graphs G with |V(G)| = n, diam(G)≥3 and clique number ω(G) = n- s for 1≤s≤4. 展开更多
关键词 vertex-coloring vertex rainbow connection number clique number
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