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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2012: Graph-Theoretic Concepts in Computer Science pp 286–296Cite as

On the Recognition of k-Equistable Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7551))

Abstract

A graph G = (V,E) is called equistable if there exist a positive integer t and a weight function \(w:V \longrightarrow \mathbb{N}\) such that S ⊆ V is a maximal stable set of G if and only if w(S) = t. The function w, if exists, is called an equistable function of G. No combinatorial characterization of equistable graphs is known, and the complexity status of recognizing equistable graphs is open. It is not even known whether recognizing equistable graphs is in NP.

Let k be a positive integer. An equistable graph G = (V,E) is said to be k-equistable if it admits an equistable function which is bounded by k. For every constant k, we present a polynomial time algorithm which decides whether an input graph is k-equistable.

MM is supported in part by “Agencija za raziskovalno dejavnost Republike Slovenije”, research program P1–0285 and research projects J1–4010, J1–4021 and N1–0011. Research was partly done during a visit of the second author at the Department of Computer Science and Mathematics at the Ariel University Center of Samaria in the frame of a Slovenian Research Agency project MU-PROM/11-007. The second author thanks the Department for its hospitality and support.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, 40700, Israel

    Vadim E. Levit & David Tankus

  2. University of Primorska, UP IAM, Muzejski trg 2, SI6000, Koper, Slovenia

    Martin Milanič

  3. University of Primorska, UP FAMNIT, Glagoljaška 8, SI6000, Koper, Slovenia

    Martin Milanič

Authors
  1. Vadim E. Levit
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  2. Martin Milanič
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  3. David Tankus
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Caesarea Rothschild Institute (CRI), 31905, Haifa, Israel

    Martin Charles Golumbic

  2. The Academic College of Tel Aviv, Unit of Statistics and Probability Studies, 64044, Yaffo, Israel

    Michal Stern

  3. Shenkar College and Caesarea Rothschild Institute (CRI), University of Haifa, 31905, Haifa, Israel

    Avivit Levy

  4. Caesarea Rothschild Institute (CRI), 31905, Haifa, Israel

    Gila Morgenstern

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Levit, V.E., Milanič, M., Tankus, D. (2012). On the Recognition of k-Equistable Graphs. In: Golumbic, M.C., Stern, M., Levy, A., Morgenstern, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2012. Lecture Notes in Computer Science, vol 7551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34611-8_29

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  • DOI: https://doi.org/10.1007/978-3-642-34611-8_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34610-1

  • Online ISBN: 978-3-642-34611-8

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