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Dense graphs with small clique number

✍ Scribed by Wayne Goddard; Jeremy Lyle


Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
121 KB
Volume
66
Category
Article
ISSN
0364-9024

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πŸ“œ SIMILAR VOLUMES


Dominating sets with small clique coveri
✍ Penrice, Stephen G. πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 84 KB πŸ‘ 2 views

Motivated by earlier work on dominating cliques, we show that if a graph G is connected and contains no induced subgraph isomorphic to P 6 or H t (the graph obtained by subdividing each edge of K 1,t , t β‰₯ 3, by exactly one vertex), then G has a dominating set which induces a connected graph with cl

On connectivity in graphs with given cli
✍ Angelika Hellwig; Lutz Volkmann πŸ“‚ Article πŸ“… 2006 πŸ› John Wiley and Sons 🌐 English βš– 82 KB πŸ‘ 1 views

## Abstract We consider finite, undirected, and simple graphs __G__ of order __n__(__G__) and minimum degree Ξ΄(__G__). The connectivity ΞΊ(__G__) for a connected graph __G__ is defined as the minimum cardinality over all vertex‐cuts. If ΞΊ(__G__) < δ(__G__), then Topp and Volkmann 7 showed in 1993 f

On local connectivity of graphs with giv
✍ Andreas Holtkamp; Lutz Volkmann πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 72 KB

## Abstract For a vertex __v__ of a graph __G__, we denote by __d__(__v__) the __degree__ of __v__. The __local connectivity__ ΞΊ(__u, v__) of two vertices __u__ and __v__ in a graph __G__ is the maximum number of internally disjoint __u__ –__v__ paths in __G__, and the __connectivity__ of __G__ is

On the Ramsey number of trees versus gra
✍ Ronald J. Gould; Michael S. Jacobson πŸ“‚ Article πŸ“… 1983 πŸ› John Wiley and Sons 🌐 English βš– 335 KB

Chvatal established that r(T,, K,,) = (m -1 ) ( n -1 ) + 1, where T, , , is an arbitrary tree of order m and K, is the complete graph of order n. This result was extended by Chartrand, Gould, and Polimeni who showed K, could be replaced by a graph with clique number n and order n + 5 provided n 2 3

On graphs with small Ramsey numbers
✍ A. V. Kostochka; V. RΓΆdl πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 88 KB

## Abstract Let __R__(__G__) denote the minimum integer __N__ such that for every bicoloring of the edges of __K~N~__, at least one of the monochromatic subgraphs contains __G__ as a subgraph. We show that for every positive integer __d__ and each Ξ³,0 < γ < 1, there exists __k__ = __k__(__d__,Ξ³) su

Fractional chromatic number and circular
✍ Daphne Der-Fen Liu; Xuding Zhu πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 136 KB

## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329–330, 2005. Let __M__ be a set of positive integers. The distance graph generated by __M__, denoted by __G__(__Z, M__), has the set __Z__ of all integers as the vertex set, and edges __ij__ whenever |__i__