3连通直径3图的边数

7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings. Pub Date : 2004-05-10 DOI:10.1109/ISPAN.2004.1300506

Ming-Chun Tsai, H. Fu

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引用次数: 0

摘要

设衰减数/spl zeta/(G)为连通图G的协树的最小分量数，设/spl ω /为所有3连通直径3图的集合。在本文中，我们证明了如果k是使得每一个(p,q)-图G /spl epsi/ /spl Omega/的q /spl zeta/(H) /spl lles / l - 1的最小数，并且1是使得每一个(p,q)-图G /spl epsi/ /spl Omega/的/spl zeta/(H) /spl lles / l - 1的最小数，那么k= 1。进一步，我们证明了k /spl小于/ 11，并找到了一个3连通的，直径为3的图，其q = 2p - 8。所以我们有8 /s / k /s / 11我们推测k = 8。

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Edge number of 3-connected diameter 3 graphs

Let the decay number, /spl zeta/(G) be the minimum number of components of a cotree of a connected graph G. Let /spl Omega/ be the collection of all 3-connected diameter 3 graphs. In this paper, we prove that if k is the minimum number such that q /spl ges/ 2p - k for each (p,q)-graph G /spl epsi/ /spl Omega/, and 1 is the minimum number such that /spl zeta/(H) /spl les/ l - 1 for each graph H /spl epsi/ /spl Omega/, then k=l. Furthermore, we prove that k /spl les/ 11 and we find a 3-connected, diameter 3 graph with q = 2p - 8. So we have that 8 /spl les/ k /spl les/ 11 and we conjecture that k = 8.

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7th International Symposium on Parallel Architectures, Algorithms and Networks, 2004. Proceedings.

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