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ALGORITHMICA

2011

12 years 28 days 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

12 years 4 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

12 years 5 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

12 years 5 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

12 years 5 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

12 years 5 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

12 years 5 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

12 years 5 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

12 years 6 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 ...