We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
A set of vertices D of a graph G is geodetic if every vertex of G lies on a shortest path between two not necessarily distinct vertices in D. The geodetic number of G is the minimu...
We prove that a K4-free graph G of order n, size m and maximum degree at most three has an independent set of cardinality at least 1 7 (4n - m - - tr) where counts the number of c...
Jochen Harant, Michael A. Henning, Dieter Rautenba...
Abstract. The geometric thickness of a graph G is the minimum integer k such that there is a straight line drawing of G with its edge set partitioned into k plane subgraphs. Eppste...
Given a fixed multigraph H with V (H) = {h1, . . . , hm}, we say that a graph G is H-linked if for every choice of m vertices v1, . . . , vm in G, there exists a subdivision of H i...