The set of different cycle lengths of a graph G is denoted by C(G). We study how the distribution of C(G) depends on the minimum degree of G. We prove two results indicating that C(G) is dense in some sense. These results lead to the solution of a conjecture of Erdos and Hajnal stating that for suit
On a distribution of weather cycles by length
β Scribed by K. R. Gabriel; J. Neumann
- Publisher
- John Wiley and Sons
- Year
- 1957
- Tongue
- English
- Weight
- 371 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0035-9009
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β¦ Synopsis
Abstract
In the paper a weather cycle is defined as the combination of a wet (dry) spell with the successive dry (wet) spell. On the assumption that the lengths of wet and dry spells are independent and obey geometric distributions, the distribution function of the lengths of weather cycles is deduced and tested against observational data for Tel Aviv. The peak frequency of weatherβcycle lengths at Tel Aviv is found to be at about 4 days.
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## Abstract For a graph __G__, __p__(__G__) and __c__(__G__) denote the order of a longest path and a longest cycle of __G__, respectively. In this paper, we prove that if __G__ is a 3 βconnected graph of order __n__ such that the minimum degree sum of four independent vertices is at least __n__+ 6