Displaying similar documents to “On longest paths in connected graphs”

3-Paths in Graphs with Bounded Average Degree

Stanislav Jendrol′, Mária Maceková, Mickaël Montassier, Roman Soták (2016)

Discussiones Mathematicae Graph Theory

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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 m contains a path of one of the types [...] Moreover, no parameter of this description can be improved.