A note on maximal common subgraphs of the Dirac's family of graphs

Jozef Bucko; Peter Mihók; Jean-François Saclé; Mariusz Woźniak

ArticleOriginal scientific text

Title

A note on maximal common subgraphs of the Dirac's family of graphs

Authors ¹, ¹, ², ³

Affiliations

Technical University of Košice, Faculty of Economics, Nĕmcovej 32, 040 01 Košice, Slovakia
LRI, Bât. 490, Université de Paris-Sud, 91405 Orsay, France
AGH University of Science and Technology, Department of Applied Mathematics, Al. Mickiewicza 30, 30-059 Kraków, Poland

Abstract

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

^{2 n}

for n ≥ 2.

Keywords

ENG

maximal common subgraph, Dirac's family, Hamiltonian cycle

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O. Ore, On a graph theorem by Dirac J. Combin. Theory 2 (1967) 383-392, doi: 10.1016/S0021-9800(67)80036-X.

Title

A note on maximal common subgraphs of the Dirac's family of graphs

Affiliations

Abstract

Keywords

Bibliography