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ARSCOM
2004
14 years 10 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...
ARSCOM
2004
14 years 10 months ago
2004
All cubic partial cubes (i.e., cubic isometric subgraphs of hypercubes) up to 30 vertices and all edge-critical partial cubes up to 14 vertices are presented. The lists of graphs ...
ARSCOM
2004
14 years 10 months ago
2004
The existence question for the family of 4-(15, 5, ) designs has long been answered for all values of except = 2. Here, we resolve this last undecided case and prove that 4-(15, ...
ARSCOM
2004
14 years 10 months ago
2004
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
ARSCOM
2004
14 years 10 months ago
2004
A set of points in a Steiner triple system (STS(v)) is said to be independent if no three of these points occur in the same block. In this paper we derive for each k 8 a closed f...