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## Discussiones Mathematicae Graph Theory

2011 | 31 | 3 | 577-586
Tytuł artykułu

### Simplicial and nonsimplicial complete subgraphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Define a complete subgraph Q to be simplicial in a graph G when Q is contained in exactly one maximal complete subgraph ('maxclique') of G; otherwise, Q is nonsimplicial. Several graph classes-including strong p-Helly graphs and strongly chordal graphs-are shown to have pairs of peculiarly related new characterizations: (i) for every k ≤ 2, a certain property holds for the complete subgraphs that are in k or more maxcliques of G, and (ii) in every induced subgraph H of G, that same property holds for the nonsimplicial complete subgraphs of H.
One example: G is shown to be hereditary clique-Helly if and only if, for every k ≤ 2, every triangle whose edges are each in k or more maxcliques is itself in k or more maxcliques; equivalently, in every induced subgraph H of G, if each edge of a triangle is nonsimplicial in H, then the triangle itself is nonsimplicial in H.
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
577-586
Opis fizyczny
Daty
wydano
2011
otrzymano
2010-03-30
zaakceptowano
2010-09-02
Twórcy
autor
• Department of Mathematics & Statistics, Wright State University, Dayton, Ohio 45435, USA
Bibliografia
• [1] A. Brandstadt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey, Society for Industrial and Applied Mathematics (Philadelphia, 1999), doi: 10.1137/1.9780898719796.
• [2] M.C. Dourado, F. Protti and J.L. Szwarcfiter, On the strong p-Helly property, Discrete Appl. Math. 156 (2008) 1053-1057, doi: 10.1016/j.dam.2007.05.047.
• [3] M. Farber, Characterizations of strongly chordal graphs, Discrete Math. 43 (1983) 173-189, doi: 10.1016/0012-365X(83)90154-1.
• [4] R.E. Jamison, On the null-homotopy of bridged graphs, European J. Combin. 8 (1987) 421-428.
• [5] T.A. McKee, A new characterization of strongly chordal graphs, Discrete Math. 205 (1999) 245-247, doi: 10.1016/S0012-365X(99)00107-7.
• [6] T.A. McKee, Requiring chords in cycles, Discrete Math. 297 (2005) 182-189, doi: 10.1016/j.disc.2005.04.009.
• [7] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory, Society for Industrial and Applied Mathematics (Philadelphia, 1999).
• [8] E. Prisner, Hereditary clique-Helly graphs, J. Combin. Math. Combin. Comput. 14 (1993) 216-220.
• [9] W.D. Wallis and G.-H. Zhang, On maximal clique irreducible graphs, J. Combin. Math. Combin. Comput. 8 (1993) 187-193.
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Bibliografia
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