ALGORITHMICA
2011
12 years 11 months ago
2011
We show that computing the crossing number and the odd crossing number of a graph with a given rotation system is NP-complete. As a consequence we can show that many of the well-k...
GC
2010
Springer
13 years 3 months ago
2010
Springer
The b-chromatic number of a graph G is the largest integer k such that G admits a proper k-coloring in which every color class contains at least one vertex adjacent to some vertex...
SIAMDM
2002
13 years 4 months ago
2002
Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. Combinatorial reductions are used to derive a second order, linear homogeneous differential equation with polyno...
COMBINATORICS
1998
13 years 4 months ago
1998
The aim of this paper is to give a coherent account of the problem of constructing cubic graphs with large girth. There is a well-defined integer µ0(g), the smallest number of v...
DM
2002
13 years 4 months ago
2002
In 1993, Brualdi and Massey conjectured that every graph can be incidence colored with + 2 colors, where is the maximum degree of a graph. Although this conjecture was solved in ...
DAM
2000
13 years 4 months ago
2000
We prove that there is no cubic graph with diameter 4 on 40 vertices. This implies that the maximal number of vertices of a (3,4)-graph is 38. ? 2000 Elsevier Science B.V. All rig...
ARSCOM
2004
13 years 4 months ago
2004
We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this the...
DM
2006
13 years 4 months ago
2006
In this paper we continue our investigations from [HM01] regarding spanning subgraphs which imply the existence of cycle double covers. We prove that if a cubic graph G has a spann...
GC
2008
Springer
13 years 4 months ago
2008
Springer
We prove that for graphs of order n, minimum degree 2 and girth g 5 the domination number satisfies 1 3 + 2 3g n. As a corollary this implies that for cubic graphs of order n ...