maximum independent setTuran graphWe characterize the connected graphs of given ordernand given independence number alpha that maximize the number of maximum independent sets. For3 <=alpha <= n/2, there is a unique such graph that arises from the disjoint union of alpha cliques of orders left ...
We show that, assuming FII, a parameterization by the size of a modulator to bounded treedepth allows for linear kernels in linear time on graph classes of bounded expansion. The same parameter yields almost-linear kernels on nowhere dense graph classes, which strictly contain those of bounded ...
A maximum clique-independent set MCI( G) of G is a set of maximum number of pairwise vertex-disjoint maximal cliques. We prove that the problem of ... V Guruswami,CP Rangan - 《Discrete Applied Mathematics》 被引量: 191发表: 2000年 The number of maximal independent sets in a connected...
To overcome the impracticalities stemming from the clique’s overly conservative nature, alternative graph-theoretic models have been introduced in the literature. The s-clique model, first introduced by Luce (1950), relaxes the requirement of direct interaction. Associating the number of intermediary ...
B. Yilma, The maximum number of K3-free and K4-free edge 4-colorings, submitted. 1 27. V. R¨odl and M. Schacht, Regular partitions of hypergraphs: counting lemmas, Combin. Probab. Comput. 16 (2007), no. 6, 887–901. 17 28. , Regular partitions of hypergraphs: regularity lemmas...
A graph is $k$-degenerate if there exists an ordering of its vertices $v_{1},...,v_{n}$ such that $|N(v_{i})\cap V_{i}|\leq k $. Our contribution is an algorithm computing a maximum clique for this class of graphs in time $O(1.2127^{k}(n-k+1))$, thus improving ...
It was recently proved that any graph satisfying $\omega > \frac 23(\Delta+1)$ contains a stable set hitting every maximum clique. In this note we prove that the same is true for graphs satisfying $\omega \geq \frac 23(\Delta+1)$ unless the graph is the strong product of $K_{\...
“cohesiveness” characteristics than other existing clique relaxation models in some worst-case scenarios. The main focus of the paper is on the problem of finding a small-world subgraph of maximum cardinality in a given graph. We describe a mixed integer programming (MIP) formulation of the ...
Under a Creative Commons license open accessAbstract For k≥1, the k-independence number αk of a graph is the maximum number of vertices that are mutually at distance greater than k. The well-known inertia and ratio bounds for the (1-)independence number α(=α1) of a graph, due to...
摘要原文 We show that in contrast to the Rado graph, the Henson graphs are not computably indivisible. 展开全部 机器翻译 AI理解论文&经典十问 挑战十问 Request failed with status code 503 图表提取 Request failed with status code 503 阅读PDFCAS-3JCR-Q1SCIE ...