3-path in graphs with bounded average degree

Stanislav Jendrol 1 Mária Maceková Mickaël Montassier 2 Roman Soták 1
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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.
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Submitted on : Tuesday, July 19, 2016 - 1:46:59 PM
Last modification on : Thursday, May 24, 2018 - 3:59:22 PM

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

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