The interval number of a graph G, denoted i(G), is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t compact real intervals. It is known that every planar graph has interval number at most 3 and that this result is best possible. We investiga
Bounds for the genus of graphs with given Betti number
โ Scribed by Martin Milgram; Peter Ungar
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 342 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract In this article we first give an upper bound for the chromatic number of a graph in terms of its degrees. This bound generalizes and modifies the bound given in 11. Next, we obtain an upper bound of the order of magnitude ${\cal O}({n}^{{1}-\epsilon})$ for the coloring number of a graph
The average orientable genus of graphs has been the subject of a considerable number of recent investigations. It is the purpose of this article to examine the extent to which the average genus of the amalgamation of graphs fails to be additive over its constituent subgraphs. This discrepancy is bou
The maximum number of cutvertices in a connected graph of order n having minimum degree at least 6 is determined for 6 > 5.