Online Dominating Set and Variations on Restricted Graph Classes
نویسنده
چکیده
We study online versions ofMinimum Dominating Set Min imum Connected Dominating Set andMinimum Independent Dom inating Set where we restrict the input graphs to belong to a certain graph class after each insertion step We show that straight forward and easy to implement online strategies achieve optimum or nearly optimum competitive ratios for trees unit disk graphs and bounded degree graphs for standard and independent dominating sets For connected dominating sets our results are not tight and thus provide challenges for future re search In an orthogonal approach we show that for many graph classes such as planar bipartite and bounded treewidth graphs the optimum achievable competitive ratios are n where n is the number of graph vertices
منابع مشابه
On the Maximum Number of Dominating Classes in Graph Coloring
In this paper we investigate the dominating- -color number، of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].
متن کاملIndependent domination in directed graphs
In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...
متن کاملdominating subset and representation graph on topological spaces
Let a topological space. An intersection graph on a topological space , which denoted by , is an undirected graph which whose vertices are open subsets of and two vertices are adjacent if the intersection of them are nonempty. In this paper, the relation between topological properties of and graph properties of are investigated. Also some classifications and representations for the graph ...
متن کاملA Boundary Property for Upper Domination
An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard, but can be solved in polynomial time in some restricted graph classes, such as P4-free graphs or 2K2-free graphs. For classes defined by finitely many forbidden induced subgraphs, the boundary separating diffi...
متن کاملSome Results on the Maximal 2-Rainbow Domination Number in Graphs
A 2-rainbow dominating function ( ) of a graph is a function from the vertex set to the set of all subsets of the set such that for any vertex with the condition is fulfilled, where is the open neighborhood of . A maximal 2-rainbow dominating function on a graph is a 2-rainbow dominating function such that the set is not a dominating set of . The weight of a maximal is the value . ...
متن کامل