Graphs with 6-Ways
| Autor: | John L. Leonard |
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| Rok vydání: | 1973 |
| Předmět: | |
| Zdroj: | Canadian Journal of Mathematics. 25:687-692 |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/cjm-1973-069-x |
| Popis: | In a finite graph with no loops nor multiple edges, two points a and b are said to be connected by an r-way, or more explicitly, by a line r-way a — b if there are r paths, no two of which have lines in common (although they may share common points), which join a to b. In this note we demonstrate that any graph with n points and 3n — 2 or more lines must contain a pair of points joined by a 6-way, and that 3n — 2 is the minimum number of lines which guarantees the presence of a 6-way in a graph of n points.In the language of [3], this minimum number of lines needed to guarantee a 6-way is denoted U(n). For the background of this problem, the reader is referred to [3]. |
| Databáze: | OpenAIRE |
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