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Journal Articles Discussiones Mathematicae Graph Theory Year : 2016

3-path in graphs with bounded average degree

Abstract

In this paper we study the existence of unavoidable paths on three vertices in sparse graphs. A path uvw on three vertices u, v, and w is of type (i,j, k) if the degree of u (respectively v, w) is at most i (respectively j, k). We prove that every graph with minimum degree at least 2 and average degree strictly less than to contains a path of one of the types (Equation presented) Moreover, no parameter of this description can be improved.

Dates and versions

lirmm-01346642 , version 1 (19-07-2016)

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Stanislav Jendrol, Mária Maceková, Mickaël Montassier, Roman Soták. 3-path in graphs with bounded average degree. Discussiones Mathematicae Graph Theory, 2016, 36 (2), pp.339-353. ⟨10.7151/dmgt.1859⟩. ⟨lirmm-01346642⟩
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