JGT
2007
13 years 4 months ago
2007
: A (directed) cycle C in a graph is called consistent provided there exists an automorphism of , acting as a 1-step rotation of C. A beautiful but not well-known result of J.H. Co...
JGT
2007
13 years 4 months ago
2007
It is known that for every integer k ≥ 4, each k-map graph with n vertices has at most kn − 2k edges. Previously, it was open whether this bound is tight or not. We show that ...
JGT
2007
13 years 4 months ago
2007
We introduce and study backbone colorings, a variation on classical vertex colorings: Given a graph G = (V, E) and a spanning subgraph H of G (the backbone of G), a backbone color...
JGT
2007
13 years 4 months ago
2007
JGT
2007
13 years 4 months ago
2007
We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved...
JGT
2007
13 years 4 months ago
2007
JGT
2007
13 years 4 months ago
2007
: Let G be a graph with maximum degree d ≥ 3 and ω(G) ≤ d, where ω(G) is the clique number of the graph G. Let p1 and p2 be two positive integers such that d = p1 + p2. In th...
JGT
2007
13 years 4 months ago
2007
JGT
2007
13 years 4 months ago
2007
: We present a planar hypohamiltonian graph on 48 vertices, and derive some consequences. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 338–342, 2007
JGT
2007
13 years 4 months ago
2007
: Let G be a 3-connected planar graph and G∗ be its dual. We show that the pathwidth of G∗ is at most 6 times the pathwidth of G. We prove this result by relating the pathwidth...