Sum-perfect graphs

Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α(H)+ω(H)≥|V(H)|. (Here α and ω denote the stability number and clique number, respectively.) We give a set of 27 graphs and we prove that a graph G is s...

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Published inDiscrete Applied Mathematics Vol. 259; pp. 232 - 239
Main Authors Litjens, Bart, Polak, Sven, Sivaraman, Vaidy
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 30.04.2019
Elsevier BV
Subjects
Clique
Forbidden induced subgraph
Graph theory
Graphs
Perfect graph
Stable set
Sum-perfect graph
Forbidden induced subgraph
Clique
Stable set
Sum-perfect graph
Perfect graph
Online AccessGet full text
ISSN0166-218X
1872-6771
DOI10.1016/j.dam.2018.12.015

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Abstract Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α(H)+ω(H)≥|V(H)|. (Here α and ω denote the stability number and clique number, respectively.) We give a set of 27 graphs and we prove that a graph G is sum-perfect if and only if G does not contain any of the graphs in the set as an induced subgraph.
AbstractList Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α (H) + w (H) ≥ |V (H)|. (Here α and w denote the stability number and clique number, respectively.) We give a set of 27 graphs and we prove that a graph G is sum-perfect if and only if G does not contain any of the graphs in the set as an induced subgraph.
Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α(H)+ω(H)≥|V(H)|. (Here α and ω denote the stability number and clique number, respectively.) We give a set of 27 graphs and we prove that a graph G is sum-perfect if and only if G does not contain any of the graphs in the set as an induced subgraph.
Author Polak, Sven
Litjens, Bart
Sivaraman, Vaidy
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10.1016/j.tcs.2005.08.038
10.1016/0095-8956(72)90045-7
10.1016/0012-365X(86)90097-X
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10.4007/annals.2006.164.51
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Keywords Forbidden induced subgraph
Clique
Stable set
Sum-perfect graph
Perfect graph
Language English
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References Poljak (b10) 1974; 15
Zverovich (b12) 2006; 351
Hayward (b6) 1985; 39
Lovász (b9) 1972; 13
Preissmann, de Werra, Mahadev (b11) 1986; 61
Chudnovsky, Robertson, Seymour, Thomas (b3) 2006
Hayward, Hoang, Maffray (b7) 1989; 5
Brandstädt, Le (b2) 2004; 17
Chvátal, Hammer (b4) 1973
Diestel (b5) 2010; vol. 173
R. Hayward, J. Spinrad, R. Sritharan, Weakly chordal graph algorithms via handles, in: Proc. of the 11th symposium on Discrete Algorithms, vol. 12, 2000, pp. 42–49.
Berge, Duchet (b1) 1984; 21
Berge (10.1016/j.dam.2018.12.015_b1) 1984; 21
Chvátal (10.1016/j.dam.2018.12.015_b4) 1973
Diestel (10.1016/j.dam.2018.12.015_b5) 2010; vol. 173
Zverovich (10.1016/j.dam.2018.12.015_b12) 2006; 351
Brandstädt (10.1016/j.dam.2018.12.015_b2) 2004; 17
Hayward (10.1016/j.dam.2018.12.015_b7) 1989; 5
Chudnovsky (10.1016/j.dam.2018.12.015_b3) 2006
10.1016/j.dam.2018.12.015_b8
Poljak (10.1016/j.dam.2018.12.015_b10) 1974; 15
Preissmann (10.1016/j.dam.2018.12.015_b11) 1986; 61
Hayward (10.1016/j.dam.2018.12.015_b6) 1985; 39
Lovász (10.1016/j.dam.2018.12.015_b9) 1972; 13
References_xml – reference: R. Hayward, J. Spinrad, R. Sritharan, Weakly chordal graph algorithms via handles, in: Proc. of the 11th symposium on Discrete Algorithms, vol. 12, 2000, pp. 42–49.
– volume: 13
  start-page: 95
  year: 1972
  end-page: 98
  ident: b9
  article-title: A characterization of perfect graphs
  publication-title: J. Combin. Theory Ser. B
– volume: 15
  start-page: 307
  year: 1974
  end-page: 309
  ident: b10
  article-title: A note on stable sets and coloring of graphs
  publication-title: Comment. Math. Univ. Carolin.
– volume: 61
  start-page: 259
  year: 1986
  end-page: 267
  ident: b11
  article-title: A note on superbrittle graphs
  publication-title: Discrete Math.
– year: 1973
  ident: b4
  article-title: Set-packing and threshold graphs
  publication-title: Univ. Waterloo Res. Report CORR
– volume: 351
  start-page: 47
  year: 2006
  end-page: 56
  ident: b12
  article-title: Satgraphs and independent domination. Part 1
  publication-title: Theoret. Comput. Sci.
– volume: 21
  start-page: 57
  year: 1984
  end-page: 61
  ident: b1
  article-title: Strongly perfect graphs, topics on perfect graphs
  publication-title: Ann. Disc. Math.
– start-page: 51
  year: 2006
  end-page: 229
  ident: b3
  article-title: The strong perfect graph theorem
  publication-title: Ann. Math.
– volume: vol. 173
  year: 2010
  ident: b5
  publication-title: Graph Theory
– volume: 39
  start-page: 200
  year: 1985
  end-page: 208
  ident: b6
  article-title: Weakly triangulated graphs
  publication-title: J. Combin. Theory Ser. B
– volume: 5
  start-page: 339
  year: 1989
  end-page: 349
  ident: b7
  article-title: Optimizing weakly triangulated graphs
  publication-title: Graphs Combin.
– volume: 17
  start-page: 341
  year: 2004
  end-page: 360
  ident: b2
  article-title: Split-perfect graphs: characterizations and algorithmic use
  publication-title: SIAM J. Discr. Math.
– ident: 10.1016/j.dam.2018.12.015_b8
– volume: 39
  start-page: 200
  year: 1985
  ident: 10.1016/j.dam.2018.12.015_b6
  article-title: Weakly triangulated graphs
  publication-title: J. Combin. Theory Ser. B
  doi: 10.1016/0095-8956(85)90050-4
– volume: vol. 173
  year: 2010
  ident: 10.1016/j.dam.2018.12.015_b5
– volume: 351
  start-page: 47
  year: 2006
  ident: 10.1016/j.dam.2018.12.015_b12
  article-title: Satgraphs and independent domination. Part 1
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2005.08.038
– volume: 13
  start-page: 95
  year: 1972
  ident: 10.1016/j.dam.2018.12.015_b9
  article-title: A characterization of perfect graphs
  publication-title: J. Combin. Theory Ser. B
  doi: 10.1016/0095-8956(72)90045-7
– volume: 61
  start-page: 259
  year: 1986
  ident: 10.1016/j.dam.2018.12.015_b11
  article-title: A note on superbrittle graphs
  publication-title: Discrete Math.
  doi: 10.1016/0012-365X(86)90097-X
– volume: 17
  start-page: 341
  year: 2004
  ident: 10.1016/j.dam.2018.12.015_b2
  article-title: Split-perfect graphs: characterizations and algorithmic use
  publication-title: SIAM J. Discr. Math.
  doi: 10.1137/S0895480100367676
– start-page: 51
  year: 2006
  ident: 10.1016/j.dam.2018.12.015_b3
  article-title: The strong perfect graph theorem
  publication-title: Ann. Math.
  doi: 10.4007/annals.2006.164.51
– volume: 21
  start-page: 57
  year: 1984
  ident: 10.1016/j.dam.2018.12.015_b1
  article-title: Strongly perfect graphs, topics on perfect graphs
  publication-title: Ann. Disc. Math.
– volume: 5
  start-page: 339
  year: 1989
  ident: 10.1016/j.dam.2018.12.015_b7
  article-title: Optimizing weakly triangulated graphs
  publication-title: Graphs Combin.
  doi: 10.1007/BF01788689
– volume: 15
  start-page: 307
  year: 1974
  ident: 10.1016/j.dam.2018.12.015_b10
  article-title: A note on stable sets and coloring of graphs
  publication-title: Comment. Math. Univ. Carolin.
– year: 1973
  ident: 10.1016/j.dam.2018.12.015_b4
  article-title: Set-packing and threshold graphs
  publication-title: Univ. Waterloo Res. Report CORR
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Snippet Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G,...
Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph G to be sum-perfect if for every induced subgraph H of G, α (H) + w...
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SubjectTerms Clique
Forbidden induced subgraph
Graph theory
Graphs
Perfect graph
Stable set
Sum-perfect graph
Title Sum-perfect graphs
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