论文标题
超级卡，阳光和毛毛虫图
Supercards, Sunshines and Caterpillar Graphs
论文作者
论文摘要
通过删除顶点V和所有Edgents dos v to V，从图G获得的顶点删除的子图G-V称为G。G的甲板是其未标记卡的多键。 The number of common cards b(G,H) of G and H is the cardinality of the multiset intersection of the decks of G and H. A supercard G+ of G and H is a graph whose deck contains at least one card isomorphic to G and at least one card isomorphic to H. We show how maximum sets of common cards of G and H correspond to certain sets of permutations of the vertices of a supercard, which we call maximum saturating 套。我们将超级卡的理论和最大饱和集的理论应用于G是阳光图，而H是毛毛虫图。我们表明，对于足够大的n，存在一些最大饱和集，其中包含至少B（g，h）-2 g+的自动形态，并且该子集始终对环状或二二二甲体组是同构。我们证明，对于足够大的n，B（g，h）<= 2（n+1）/5，并且存在一个独特的成对图，可以达到这种结合。我们进一步表明，在这种情况下，相应的最大饱和集对二面体是同构。
The vertex-deleted subgraph G-v, obtained from the graph G by deleting the vertex v and all edges incident to v, is called a card of G. The deck of G is the multiset of its unlabelled cards. The number of common cards b(G,H) of G and H is the cardinality of the multiset intersection of the decks of G and H. A supercard G+ of G and H is a graph whose deck contains at least one card isomorphic to G and at least one card isomorphic to H. We show how maximum sets of common cards of G and H correspond to certain sets of permutations of the vertices of a supercard, which we call maximum saturating sets. We apply the theory of supercards and maximum saturating sets to the case when G is a sunshine graph and H is a caterpillar graph. We show that, for large enough n, there exists some maximum saturating set that contains at least b(G,H)-2 automorphisms of G+, and that this subset is always isomorphic to either a cyclic or dihedral group. We prove that b(G,H)<=2(n+1)/5 for large enough n, and that there exists a unique family of pairs of graphs that attain this bound. We further show that, in this case, the corresponding maximum saturating set is isomorphic to the dihedral group.
