منابع مشابه
Fundamental Dominations in Graphs
Nine variations of the concept of domination in a simple graph are identified as fundamental domination concepts, and a unified approach is introduced for studying them. For each variation, the minimum cardinality of a subset of dominating elements is the corresponding fundamental domination number. It is observed that, for each nontrivial connected graph, at most five of these nine numbers can...
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An independent set (or a stable set) in a graph G is a subset of pairwise nonadjacent vertices of G. An independent set of G is maximal if it is not properly contained in any other independent set of G. The Maximum-Weight Independent Set (WIS) problem is the following: Given a graphG = (V,E) and a weight function w on V , determine an independent set of G of maximum weight. Let αw(G) denote the...
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In this paper we will study the complexity of 4-colorability in subclasses of P6-free graphs. The well known k-colorability problem is NP -complete. It has been shown that if k-colorability is solvable in polynomial time for an induced H-free graph, then every component of H is a path. Recently, Huang [11] has shown several improved complexity results on k-coloring Pt-free graphs, where Pt is a...
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The class of graphs that do not contain an induced path on k vertices, Pk-free graphs, plays a prominent role in algorithmic graph theory. This motivates the search for special structural properties of Pkfree graphs, including alternative characterizations. Let G be a connected Pk-free graph, k ≥ 4. We show that G admits a connected dominating set whose induced subgraph is either Pk−2-free, or ...
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2013
ISSN: 1225-1763
DOI: 10.4134/ckms.2013.28.4.857