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
Dense graphs with small clique number
β 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
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## 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 vertexβcuts. If ΞΊ(__G__)β<βΞ΄(__G__), then Topp and Volkmann 7 showed in 1993 f
## 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__ β__v__ paths in __G__, and the __connectivity__ of __G__ is
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
## 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 Ξ³,0β<βΞ³β<β1, there exists __k__β=β__k__(__d__,Ξ³) su
## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329β330, 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__