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A note on path domination
(2016)
Formulas in connection with parameters related to convexity of paths on three vertices: caterpillars and unit interval graphs
(The University of Queensland. Combinatorial Mathematics Society of Australasia, 2021-02)
We present formulas to compute the P3 -interval number, the P3 -hull number and the percolation time for a caterpillar, in terms of certain sequences associated with it. In addition, we find a connection between the ...
End vertices in containment interval graphs
(Sociedade Brasileira de Matematica, 2017-11)
An interval containment model of a graph maps vertices intointervals of a line in such a way that two vertices are adjacent ifand only if the corresponding intervals are comparable under theinclusion relation. Graphs ...
New algorithms for weighted k-domination and total k-domination problems in proper interval graphs
(Elsevier Science, 2019-11)
Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set is a set of vertices such that every ...
On the graph on a weyl group being an interval graph
(Universidad Nacuional de Colombia; Sociedad Colombiana de matemáticas, 1998)
We consider the graph on a Weyl group whose associated root system is arbitrary. It is shown that such a graph is an interval graph only when the associated root systems are of some particular types.
Improved algorithms for k-domination and total k-domination in proper interval graphs
(Springer, 2018-07)
Given a positive integer k, a k-dominating set in a graph G is a set of vertices such that every vertex not in the set has at least k neighbors in the set. A total k-dominating set, also known as a k-tuple total dominating ...
A faster algorithm for the cluster editing problem on proper interval graphs
(Elsevier Science, 2015-12)
We develop a linear-space O(n+m) time algorithm to solve the cluster editing problem for proper interval models, where n and m are the number of vertices and edges of the represented graph.
On coloring problems with local constraints
(Elsevier, 2012-04)
We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a ...
Minimal proper interval completions
(2006)
Given an arbitrary graph G=(V,E) and a proper interval graph H=(V,F) with E ⊆ F we say that H is a proper interval completion of G. The graph H is called a minimal proper interval completion of G if, for any sandwich ...