Geodesic
A note on maximal common subgraphs of the Dirac's family of graphs
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 385-390.

Voir la notice de l'article provenant de la source Library of Science

Let ⁿ be a given set of unlabeled simple graphs of order n. A maximal common subgraph of the graphs of the set ⁿ is a common subgraph F of order n of each member of ⁿ, that is not properly contained in any larger common subgraph of each member of ⁿ. By well-known Dirac's Theorem, the Dirac's family ⁿ 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 ^2n for n ≥ 2.
Keywords: maximal common subgraph, Dirac's family, Hamiltonian cycle 
@article{DMGT_2005_25_3_a14,
     author = {Bucko, Jozef and Mih\'ok, Peter and Sacl\'e, Jean-Fran\c{c}ois and Wo\'zniak, Mariusz},
     title = {A note on maximal common subgraphs of the {Dirac's} family of graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {385--390},
     publisher = {mathdoc},
     volume = {25},
     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a14/}
}
TY  - JOUR
AU  - Bucko, Jozef
AU  - Mihók, Peter
AU  - Saclé, Jean-François
AU  - Woźniak, Mariusz
TI  - A note on maximal common subgraphs of the Dirac's family of graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2005
SP  - 385
EP  - 390
VL  - 25
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a14/
LA  - en
ID  - DMGT_2005_25_3_a14
ER  - 
%0 Journal Article
%A Bucko, Jozef
%A Mihók, Peter
%A Saclé, Jean-François
%A Woźniak, Mariusz
%T A note on maximal common subgraphs of the Dirac's family of graphs
%J Discussiones Mathematicae. Graph Theory
%D 2005
%P 385-390
%V 25
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a14/
%G en
%F DMGT_2005_25_3_a14
Bucko, Jozef; Mihók, Peter; Saclé, Jean-François; Woźniak, Mariusz. A note on maximal common subgraphs of the Dirac's family of graphs. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 385-390. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a14/

[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.