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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 262–273Cite as

Some Hamiltonian Properties of One-Conflict Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8986))

Abstract

Dirac’s and Ore’s conditions (1952 and 1960) are well known and classical sufficient conditions for a graph to contain a Hamiltonian cycle and they are generalized in 1976 by the Bondy-Chvátal Theorem. In this paper, we add constraints, called conflicts. A conflict in a graph G is a pair of distinct edges of G. We denote by \((G,\mathcal {C}onf)\) a graph G with a set of conflicts \(\mathcal {C}onf\). A path without conflict P in \((G,\mathcal {C}onf)\) is a path P in G such that for any edges \(e,e'\) of P, \(\{e,e'\}\notin \mathcal {C}onf\). In this paper we consider graph with conflicts such that each vertex is not incident to the edges of more than one conflict. We call such graphs one-conflict graphs. We present sufficient conditions for one-conflict graphs to have a Hamiltonian path or cycle without conflict.

B. Momège has a PhD grant from CNRS and région Auvergne.

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Notes

  1. 1.

    A subgraph such that for any vertex its in-degree and its out-degree is exactly one.

References

  1. Bondy, J.A., Chvátal, V.: A method in graph theory. Discrete Math. 15, 111–135 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bondy, J.A., Murty, U.S.R.: Graph Theory. Springer, London Ltd (2010)

    Google Scholar 

  3. Dirac, G.A.: Some theorems on abstract graphs. Proc. London Math. Soc. 2, 69–81 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dvořák, Z.: Two-factors in orientated graphs with forbidden transitions. Discrete Math. 309(1), 104–112 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kanté, M.M., Laforest, C., Momège, B.: An exact algorithm to check the existence of (elementary) paths and a generalisation of the cut problem in graphs with forbidden transitions. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds.) SOFSEM 2013. LNCS, vol. 7741, pp. 257–267. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Kanté, M.M., Laforest, C., Momège, B.: Trees in graphs with conflict edges or forbidden transitions. In: Chan, T.-H.H., Lau, L.C., Trevisan, L. (eds.) TAMC 2013. LNCS, vol. 7876, pp. 343–354. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Li, H.: Generalizations of Dirac’s theorem in hamiltonian graph theory - a survey. Discrete Math. 313(19), 2034–2053 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ore, Ø.: Note on Hamiltonian circuits. Am. Math. Mon. 67, 55 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  9. Szeider, S.: Finding paths in graphs avoiding forbidden transitions. Discrete Appl. Math. 126(2–3), 261–273 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

We thank Mamadou M. Kanté and anonymous referees for reading and helping to improve a first version of this work.

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Authors and Affiliations

  1. LIMOS, CNRS UMR 6158 – Université Blaise Pascal, Clermont-Ferrand, Campus des Cézeaux, 24 Avenue des Landais, 63173, Aubiére Cedex, France

    Christian Laforest & Benjamin Momège

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  1. Christian Laforest
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  2. Benjamin Momège
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Correspondence to Benjamin Momège .

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Editors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic

    Kratochvíl Jan

  2. University of Newcastle, Newcastle, New South Wales, Australia

    Mirka Miller

  3. University of Minnesota, Duluth Department of Mathematics, Duluth, Minnesota, USA

    Dalibor Froncek

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Laforest, C., Momège, B. (2015). Some Hamiltonian Properties of One-Conflict Graphs. In: Jan, K., Miller, M., Froncek, D. (eds) Combinatorial Algorithms. IWOCA 2014. Lecture Notes in Computer Science(), vol 8986. Springer, Cham. https://doi.org/10.1007/978-3-319-19315-1_23

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  • DOI: https://doi.org/10.1007/978-3-319-19315-1_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19314-4

  • Online ISBN: 978-3-319-19315-1

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