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## Discussiones Mathematicae Graph Theory

2010 | 30 | 4 | 651-661
Tytuł artykułu

### Clique graph representations of ptolemaic graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A graph is ptolemaic if and only if it is both chordal and distance-hereditary. Thus, a ptolemaic graph G has two kinds of intersection graph representations: one from being chordal, and the other from being distance-hereditary. The first of these, called a clique tree representation, is easily generated from the clique graph of G (the intersection graph of the maximal complete subgraphs of G). The second intersection graph representation can also be generated from the clique graph, as a very special case of the main result: The maximal Pₙ-free connected induced subgraphs of the p-clique graph of a ptolemaic graph G correspond in a natural way to the maximal $P_{n+1}$-free induced subgraphs of G in which every two nonadjacent vertices are connected by at least p internally disjoint paths.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
651-661
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-04-17
poprawiono
2010-02-23
zaakceptowano
2010-03-02
Twórcy
autor
• Department of Mathematics and Statistics, Wright State University, Dayton, Ohio 45435, USA
Bibliografia
• [1] H.-J. Bandelt and E. Prisner, Clique graphs and Helly graphs, J. Combin. Theory (B) 51 (1991) 34-45, doi: 10.1016/0095-8956(91)90004-4.
• [2] B.-L. Chen and K.-W. Lih, Diameters of iterated clique graphs of chordal graphs, J. Graph Theory 14 (1990) 391-396, doi: 10.1002/jgt.3190140311.
• [3] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey, Society for Industrial and Applied Mathematics (Philadelphia, 1999).
• [4] E. Howorka, A characterization of ptolemaic graphs, J. Graph Theory 5 (1981) 323-331, doi: 10.1002/jgt.3190050314.
• [5] T.A. McKee, Maximal connected cographs in distance-hereditary graphs, Utilitas Math. 57 (2000) 73-80.
• [6] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory, Society for Industrial and Applied Mathematics (Philadelphia, 1999).
• [7] F. Nicolai, A hypertree characterization of distance-hereditary graphs, Tech. Report Gerhard-Mercator-Universität Gesamthochschule (Duisburg SM-DU-255, 1994).
• [8] E. Prisner, Graph Dynamics, Pitman Research Notes in Mathematics Series #338 (Longman, Harlow, 1995).
• [9] J.L. Szwarcfiter, A survey on clique graphs, in: Recent advances in algorithms and combinatorics, pp. 109-136, CMS Books Math./Ouvrages Math. SMC 11 (Springer, New York, 2003).
Typ dokumentu
Bibliografia
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