Abstract
Nash-Williams and Chvátal conditions (1969 and 1972) are well known and classical sufficient conditions for a graph to contain a Hamiltonian cycle. In this paper, we add constraints, called conflicts. A conflict is a pair of edges of the graph that cannot be both in a same Hamiltonian path or cycle. Given a graph G and a set of conflicts, we try to determine whether G contains such a Hamiltonian path or cycle without conflict. We focus in this paper on graphs in which each vertex is part of at most one conflict, called one-conflict graphs. We propose Nash-Williams-type and Chvátal-type results in this context.
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Laforest, C., Momège, B. (2015). Nash-Williams-type and Chvátal-type Conditions in One-Conflict Graphs. In: Italiano, G.F., Margaria-Steffen, T., Pokorný, J., Quisquater, JJ., Wattenhofer, R. (eds) SOFSEM 2015: Theory and Practice of Computer Science. SOFSEM 2015. Lecture Notes in Computer Science, vol 8939. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46078-8_27
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DOI: https://doi.org/10.1007/978-3-662-46078-8_27
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