1,305 research outputs found
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
Extremal Infinite Graph Theory
We survey various aspects of infinite extremal graph theory and prove several
new results. The lead role play the parameters connectivity and degree. This
includes the end degree. Many open problems are suggested.Comment: 41 pages, 16 figure
Generation of cubic graphs and snarks with large girth
We describe two new algorithms for the generation of all non-isomorphic cubic
graphs with girth at least which are very efficient for
and show how these algorithms can be efficiently restricted to generate snarks
with girth at least .
Our implementation of these algorithms is more than 30, respectively 40 times
faster than the previously fastest generator for cubic graphs with girth at
least 6 and 7, respectively.
Using these generators we have also generated all non-isomorphic snarks with
girth at least 6 up to 38 vertices and show that there are no snarks with girth
at least 7 up to 42 vertices. We present and analyse the new list of snarks
with girth 6.Comment: 27 pages (including appendix
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