منابع مشابه
Brick partitions of graphs
For each rational number q ≥ 1, we describe two partitions of the vertex set of a graph G, called the q-brick partition and the q-superbrick partition. The special cases when q = 1 are the partitions given by the connected components and the 2-edge-connected components of G, respectively. We obtain structural results on these partitions and describe their relationship to the principal partition...
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A set $S = {u_1,u_2, ldots, u_t}$ of vertices of $G$ is an efficientdominating set if every vertex of $G$ is dominated exactly once by thevertices of $S$. Letting $U_i$ denote the set of vertices dominated by $u_i$%, we note that ${U_1, U_2, ldots U_t}$ is a partition of the vertex setof $G$ and that each $U_i$ contains the vertex $u_i$ and all the vertices atdistance~1 from it in $G$. In this ...
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Let G be a graph and n ≥ 2 an integer. We prove that the following are equivalent: (i) there is a partition (V1, . . . , Vm) of V (G) such that each Vi induces one of stars K1,1, . . . ,K1,n, and (ii) for every subset S of V (G), G\S has at most n|S| components with the property that each of their blocks is an odd order complete graph.
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The problem of finding good lower bounds on the size of the largest bipartite subgraph of a given graph has received a fair amount of attention. In particular, improving a result of Erdős ([10]; see also [11] for related problems), Edwards [9] proved the essentially best possible assertion that every graph with n vertices and m edges has a bipartite subgraph with at least m/2 + (n − 1)/4 edges....
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Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms. They are described by a pattern, usually viewed as a symmetric {0, 1, ∗}matrix M . Existing results focus on recognition algorithms and characterization theorems for graphs that admit such M -partitions, or M partitions in which vertices of the input graph G have lists...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.09.034