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ARSCOM
2004
13 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...
ARSCOM
2004
13 years 5 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
13 years 5 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
13 years 5 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
13 years 5 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...