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12 years 28 days ago
Crossing Numbers of Graphs with Rotation Systems
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...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
12 years 4 months ago
The b-Chromatic Number of Cubic Graphs
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...
Marko Jakovac, Sandi Klavzar
124views more  SIAMDM 2002»
12 years 5 months ago
Counting Claw-Free Cubic Graphs
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...
Edgar M. Palmer, Ronald C. Read, Robert W. Robinso...
99views more  COMBINATORICS 1998»
12 years 5 months ago
Constructions for Cubic Graphs with Large Girth
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...
Norman Biggs
84views more  DM 2002»
12 years 5 months ago
On incidence coloring for some cubic graphs
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 ...
Wai Chee Shiu, Peter Che Bor Lam, Dong-Ling Chen
78views more  DAM 2000»
12 years 5 months ago
Maximal cubic graphs with diameter 4
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...
Dominique Buset
104views more  ARSCOM 2004»
12 years 5 months ago
Complete Minors in Cubic Graphs with few short Cycles and Random Cubic Graphs
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...
Klas Markstrom
101views more  DM 2006»
12 years 5 months ago
Cycle double covers and spanning minors II
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...
Roland Häggkvist, Klas Markström
12 years 6 months ago
Domination in Graphs of Minimum Degree at least Two and Large Girth
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 ...
Christian Löwenstein, Dieter Rautenbach