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

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

Discussiones Mathematicae Graph Theory (2005)

  • Volume: 25, Issue: 3, page 385-390
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Jozef Bucko, et al. "A note on maximal common subgraphs of the Dirac's family of graphs." Discussiones Mathematicae Graph Theory 25.3 (2005): 385-390. <http://eudml.org/doc/270422>.

@article{JozefBucko2005,
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 $ ^\{2n\}$ for n ≥ 2.},
author = {Jozef Bucko, Peter Mihók, Jean-François Saclé, Mariusz Woźniak},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {maximal common subgraph; Dirac's family; Hamiltonian cycle},
language = {eng},
number = {3},
pages = {385-390},
title = {A note on maximal common subgraphs of the Dirac's family of graphs},
url = {http://eudml.org/doc/270422},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Jozef Bucko
AU - Peter Mihók
AU - Jean-François Saclé
AU - Mariusz Woźniak
TI - A note on maximal common subgraphs of the Dirac's family of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2005
VL - 25
IS - 3
SP - 385
EP - 390
AB - 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.
LA - eng
KW - maximal common subgraph; Dirac's family; Hamiltonian cycle
UR - http://eudml.org/doc/270422
ER -

References

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  1. [1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan, London; Elsevier, New York, 1976). Zbl1226.05083
  2. [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. Zbl0047.17001
  3. [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. [4] O. Ore, On a graph theorem by Dirac J. Combin. Theory 2 (1967) 383-392, doi: 10.1016/S0021-9800(67)80036-X. 

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