摘要:
运用图的最优填充分解定理和局部最优填充定理, 将一些特殊图类G1G2, S(G)和双圈图分解为一些可求得最小填充数的图, 得到如下结果: (1)F(PmPn)≦(m-2)(n-2), 其中m≧2, n≧2; (2)若G是有m条边的n阶2-连通图,则F(S(G))=m+F(G); (3) 设图G为双圈图,两个诱导圈的圈长分别为p和q, t为这两个圈公共部分的路上的顶点个数(不包括两个端点),则F(G)=p+q-t-6.
关键词:
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填充数 /
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分解约化 /
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弦图 /
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双圈图
Abstract:
By using the decomposition theorem and the local reductive elimination for the fill-in of graphs, the fill-in numbers of some special graphs, such as G1G2, S(G) and double cyclic graphs were studied. And the following results were obtained: (1)F(PmPn)≦(m-2)(n-2), where m≧2, n≧2; ; (2) if G is a 2-connected graph with m edges and n vertices, then F(S(G))=m+F(G); (3) let G be a double cyclic graph, the length of the two cycles being p and q, respectively, and t the number of the vertices which are both in the two cycles (the end points are excluded), then F(G)=p+q-t-6.
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