2 research outputs found
Light subgraphs in graphs with average degree at most four
A graph is said to be {\em light} in a family of graphs if
at least one member of contains a copy of and there exists
an integer such that each member of
with a copy of also has a copy of such that
for all . In this
paper, we study the light graphs in the class of graphs with small average
degree, including the plane graphs with some restrictions on girth.Comment: 12 pages, 18 figure
3-path in graphs with bounded average degree
International audienceIn 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