منابع مشابه
Dominated Colorings of Graphs
In this paper, we introduce and study a new coloring problem of a graph called the dominated coloring. A dominated coloring of a graph G is a proper vertex coloring of G such that each color class is dominated by at least one vertex of G. The minimum number of colors among all dominated colorings is called the dominated chromatic number, denoted by χdom(G). In this paper, we establish the close...
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In this article we present characterizations of locally well-dominated graphs and locally independent well-dominated graphs, and a sufficient condition for a graph to be k-locally independent well-dominated. Using these results we show that the irredundance number, the domination number and the independent domination number can be computed in polynomial time within several classes of graphs, e....
متن کاملOn hamiltonicity of P 3-dominated graphs
We introduce a new class of graphs which we call P3-dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P3-dominated graph. We prove that G is hamiltonian if α(G) ≤ κ(G), with two exceptions: K2,3 and K1,1,3. We also prove that G is hamiltonian if G is 3-connected and |V (G)| ≤ 5δ(G) − 5. These results extend known re...
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We give a characterization, in terms of forbidden induced subgraphs, of those graphs in which every connected induced subgraph has a dominating induced path on at most k vertices (k 3). We show, in particular, that k = 4 means precisely the class of domination-reducible graphs, whose original definition applied four types of structural reduction. © 2006 Elsevier B.V. All rights reserved.
متن کاملHereditarily Optimal Realizations
Acknowledgments Obviously, though by no means trivially, many thanks are due to my advisor Professor Vincent Moulton, for introducing me to this fascinating subject, providing inspiration and helping me get started. Many thanks also to my colleague and co-author Dr. Katharina Huber for her patience during the many hours we spent going over the proofs in this paper. I am also most grateful to my...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.11.044