On the recognition of k-equistable graphs

Vadim E. Levit; Martin Milanič; David Tankus

doi:10.1007/978-3-642-34611-8_29

On the recognition of k-equistable graphs

Vadim E. Levit, Martin Milanič, David Tankus

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

9 Scopus citations

Abstract

A graph G∈=∈(V,E) is called equistable if there exist a positive integer t and a weight function 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.

Original language	English
Title of host publication	Graph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers
Pages	286-296
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-34611-8_29
State	Published - 2012
Externally published	Yes
Event	38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012 - Jerusalem, Israel Duration: 26 Jun 2012 → 28 Jun 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7551 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012
Country/Territory	Israel
City	Jerusalem
Period	26/06/12 → 28/06/12

Bibliographical note

Funding Information:
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.

Keywords

equistable graph
maximal stable set
polynomial time algorithm

Access to Document

10.1007/978-3-642-34611-8_29

Cite this

Levit, V. E., Milanič, M., & Tankus, D. (2012). On the recognition of k-equistable graphs. In Graph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers (pp. 286-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7551 LNCS). https://doi.org/10.1007/978-3-642-34611-8_29

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abstract = "A graph G∈=∈(V,E) is called equistable if there exist a positive integer t and a weight function 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.",

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note = "Funding Information: 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.; 38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012 ; Conference date: 26-06-2012 Through 28-06-2012",

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Levit, VE, Milanič, M & Tankus, D 2012, On the recognition of k-equistable graphs. in Graph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7551 LNCS, pp. 286-296, 38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012, Jerusalem, Israel, 26/06/12. https://doi.org/10.1007/978-3-642-34611-8_29

On the recognition of k-equistable graphs. / Levit, Vadim E.; Milanič, Martin; Tankus, David.
Graph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers. 2012. p. 286-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7551 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Levit VE, Milanič M, Tankus D. On the recognition of k-equistable graphs. In Graph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers. 2012. p. 286-296. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-34611-8_29

On the recognition of k-equistable graphs

Abstract

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Bibliographical note

Keywords

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