Discussiones Mathematicae Graph Theory 25(3) (2005)
385-390
DOI: https://doi.org/10.7151/dmgt.1290
A NOTE ON MAXIMAL COMMON SUBGRAPHS OF THE DIRAC'S FAMILY OF GRAPHS
Jozef Bucko and Peter Mihók
Technical University of Košice
| Jean-François Saclé
LRI, Bât. 490, Université de Paris-Sud
| Mariusz Woźniak
AGH University of Science and Technology
|
Abstract
Let Fn be a given set of unlabeled simple graphs of order n. A maximal common subgraph of the graphs of the set Fn is a common subgraph F of order n of each member of Fn, that is not properly contained in any larger common subgraph of each member of Fn. By well-known Dirac's Theorem, the Dirac's family DFn of the graphs of order n and minimum degree δ ≥ [n/2] has a maximal common subgraph containing Cn. In this note we study the problem of determining all maximal common subgraphs of the Dirac's family DF2n for n ≥ 2.Keywords: maximal common subgraph, Dirac's family, Hamiltonian cycle.
2000 Mathematics Subject Classification: 05C75, 05C45.
References
[1] | J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London; Elsevier, New York, 1976). |
[2] | G.A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. (3) 2 (1952) 69-81, doi: 10.1112/plms/s3-2.1.69. |
[3] | V. Chvátal, New directions in Hamiltonian graph theory in: New Directions in the Theory of Graphs (Academic Press, New York, 1973) 65-95. |
[4] | O. Ore, On a graph theorem by Dirac J. Combin. Theory 2 (1967) 383-392, doi: 10.1016/S0021-9800(67)80036-X. |
Received 22 June 2004
Revised 13 June 2005
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