The 3-rainbow index and connected dominating sets
نویسندگان
چکیده
منابع مشابه
Rainbow Connection Number and Connected Dominating Sets
Rainbow connection number rc(G) of a connected graph G is the minimum number of colours needed to colour the edges of G, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we show that for every connected graph G, with minimum degree at least 2, the rainbow connection number is upper bounded by γc(G) + 2, where γc(G) is th...
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The proper connection number pc(G) of a connected graph G is defined as the minimum number of colors needed to color its edges, so that every pair of distinct vertices of G is connected by at least one path in G such that no two adjacent edges of the path are colored the same, and such a path is called a proper path. In this paper, we show that for every connected graph with diameter 2 and mini...
متن کاملThe complexity of connected dominating sets and total dominating sets with specified induced subgraphs
Given a graph class G, it is natural to ask (i) whether a given graph G has a connected or a total dominating set whose induced subgraph is a member of G and (ii) whether G has such a set of cardinality at most a given threshold. We give sufficient conditions on G under which these two problems are NP-hard. This condition is fulfilled in a wide variety of classes of graphs.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Optimization
سال: 2014
ISSN: 1382-6905,1573-2886
DOI: 10.1007/s10878-014-9815-0