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Recognizing Well Covered Graphs of Families with Special P 4-Components

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Abstract

A graph G is called well covered if every two maximal independent sets of G have the same number of vertices. In this paper we shall use the modular and primeval decomposition techniques to decide well coveredness of graphs such that, either all their P 4-connected components (in short, P 4-components) are separable or they belong to well known classes of graphs that, in some local sense, contain few P 4’s. In particular, we shall consider the class of cographs, P 4-reducible, P 4-sparse, extended P 4-reducible, extended P 4-sparse graphs, P 4-extendible graphs, P 4-lite graphs, and P 4-tidy graphs.

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Authors and Affiliations

  1. IM, COPPE/Sistemas, Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil

    S. Klein

  2. Instituto de Computação, Universidade de Campinas (UNICAMP), Campinas, Brazil

    C. P. de Mello

  3. Dipartimento di Matematica, Università di Roma “La Sapienza”, Roma, Italy

    A. Morgana

Authors
  1. S. Klein
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  2. C. P. de Mello
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  3. A. Morgana
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Corresponding author

Correspondence to C. P. de Mello.

Additional information

This research was partially supported by CNPq and FAPERJ.

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Klein, S., de Mello, C.P. & Morgana, A. Recognizing Well Covered Graphs of Families with Special P 4-Components. Graphs and Combinatorics 29, 553–567 (2013). https://doi.org/10.1007/s00373-011-1123-1

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  • DOI: https://doi.org/10.1007/s00373-011-1123-1

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