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231.
In our paper 1 we gave a classification of geodetic blocks of diameter two, but the proof was incorrect. Here we point out this error and give a new result about constructing geodetic blocks of diameter two. © 2004 Wiley Periodicals, Inc. J Graph Theory 46 : 79–80, 2004 相似文献
232.
Results of Lovász (1972) and Padberg (1974) imply that partitionable graphs contain all the potential counterexamples to Berge's famous Strong Perfect Graph Conjecture. A recursive method of generating partitionable graphs was suggested by Chvátal, Graham, Perold, and Whitesides (1979). Results of Seb? (1996) entail that Berge's conjecture holds for all the partitionable graphs obtained by this method. Here we suggest a more general recursion. Computer experiments show that it generates all the partitionable graphs with ω=3,α ≤ 9 (and we conjecture that the same will hold for bigger α, too) and many but not all for (ω,α)=(4,4) and (4,5). Here, α and ω are respectively the clique and stability numbers of a partitionable graph, that is the numbers of vertices in its maximum cliques and stable sets. All the partitionable graphs generated by our method contain a critical ω‐clique, that is an ω‐clique which intersects only 2ω?2 other ω‐cliques. This property might imply that in our class there are no counterexamples to Berge's conjecture (cf. Seb? (1996)), however this question is still open. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 259–285, 2002 相似文献
233.
234.
Jonas Hasselberg Panos M. Pardalos George Vairaktarakis 《Journal of Global Optimization》1993,3(4):463-482
In the last years many algorithms have been proposed for solving the maximum clique problem. Most of these algorithms have been tested on randomly generated graphs. In this paper we present different test problem generators that arise from a variety of practical applications, as well as graphs with known maximum cliques. In addition, we provide computational experience with two exact algorithms using the generated test problems. 相似文献
235.
李凤高 《高校应用数学学报(英文版)》2003,18(2)
Let AG(n,Fq) be the n-dimensional affine space over Fq,where Fq is a finite field with q elements. Denote by Г(m) the graph induced by m-flats of AG(n,Fq). For any two adjacent vertices E and F of Гr(m) ,Г(m) (E)∩ Г(m) (F) is studied. In particular,sizes of maximal cliques in Г(m) are determined and it is shown that Г(m) is not edge-regular when m＜n-1. 相似文献
236.
237.
柳柏濂 《数学物理学报(A辑)》2009,29(2):233-238
讨论了由D.Stevanovi′c提出的给定顶点数n 和最大度?的非正则图的谱半径的上界,并给出了一些新的由?表示的谱半径的界. 相似文献
238.
一个图的Wiener指数是指这个图中所有点对的距离和.Wiener指数在理论化学中有广泛应用. 本文刻画了给定顶点数及特定参数如色数或团数的图中Wiener指数达最小值的图, 同时也刻画了给定顶点数及团数的图中Wiener指数达最大值的图. 相似文献
239.
Wieslaw Kubis 《Proceedings of the American Mathematical Society》2003,131(2):619-623
A coloring of a set is any subset of , where 1$\"> is a natural number. We give some sufficient conditions for the existence of a perfect -homogeneous set, in the case where is and is a Polish space. In particular, we show that it is sufficient that there exist -homogeneous sets of arbitrarily large countable Cantor-Bendixson rank. We apply our methods to show that an analytic subset of the plane contains a perfect -clique if it contains any uncountable -clique, where is a natural number or (a set is a -clique in if the convex hull of any of its -element subsets is not contained in ).