Algorithms for the Strong Chromatic Index of Halin Graphs, Distance-Hereditary Graphs and Maximal Outerplanar Graphs

Graphs and Algorithms International audience The strong chromatic index of a graph is the minimum number of colours needed to colour the edges in such a way that each colour class is an induced matching. In this paper, we present bounds for strong chromatic index of three different products of graphs in term of the strong chromatic index of each factor. For the cartesian product of paths, cycles or complete graphs, we derive sharper results. In particular, strong chromatic indices of d-dimensional grids and of some toroidal grids are given along with approximate results on the strong chromatic index of generalized hypercubes.

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On the strong chromatic index and maximum induced matching of tree-cographs, permutation graphs and chordal bipartite graphs

Journal of Discrete Algorithms ◽

10.1016/j.jda.2014.11.004 ◽

2015 ◽

Vol 30 ◽

pp. 21-28 ◽

Cited By ~ 1

Author(s):

Ton Kloks ◽

Sheung-Hung Poon ◽

Chin-Ting Ung ◽

Yue-Li Wang

Keyword(s):

Bipartite Graphs ◽

Chromatic Index ◽

Permutation Graphs ◽

Induced Matching ◽

Strong Chromatic Index ◽

Maximum Induced Matching ◽

Chordal Bipartite Graphs

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An efficientg-centroid location algorithm for cographs

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/ijmms.2005.1405 ◽

2005 ◽

Vol 2005 (9) ◽

pp. 1405-1413 ◽

Cited By ~ 1

Author(s):

V. Prakash

Keyword(s):

Location Problem ◽

Maximum Clique ◽

Polynomial Time Algorithm ◽

Time Algorithm ◽

Outerplanar Graphs ◽

Arbitrary Graph ◽

Maximal Outerplanar Graphs ◽

Split Graphs ◽

Location Algorithm ◽

Centroid Location

In 1998, Pandu Rangan et al. Proved that locating theg-centroid for an arbitrary graph is𝒩𝒫-hard by reducing the problem of finding the maximum clique size of a graph to theg-centroid location problem. They have also given an efficient polynomial time algorithm for locating theg-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present anO(nm)time algorithm for locating theg-centroid for cographs, wherenis the number of vertices andmis the number of edges of the graph.

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Some New Classes of Open Distance-Pattern Uniform Graphs

International Journal of Combinatorics ◽

10.1155/2013/863439 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

Bibin K. Jose

Keyword(s):

Nonempty Subset ◽

Chordal Graphs ◽

Outerplanar Graph ◽

Outerplanar Graphs ◽

Induced Subgraphs ◽

Minimum Cardinality ◽

Maximal Outerplanar Graphs ◽

Split Graphs ◽

Strongly Chordal Graphs

Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern. The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). Given some property P, we establish characterization of odpu-graph with property P. In this paper, we characterize odpu-chordal graphs, and thereby characterize interval graphs, split graphs, strongly chordal graphs, maximal outerplanar graphs, and ptolemaic graphs that are odpu-graphs. We also characterize odpu-self-complementary graphs, odpu-distance-hereditary graphs, and odpu-cographs. We prove that the odpu-number of cographs is even and establish that any graph G can be embedded into a self-complementary odpu-graph H, such that G and G¯ are induced subgraphs of H. We also prove that the odpu-number of a maximal outerplanar graph is either 2 or 5.

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