Dirac's Condition for Completely Independent Spanning Trees |
| |
Authors: | Toru Araki |
| |
Institution: | DIVISION OF ELECTRONICS AND INFORMATICS, GUNMA UNIVERSITY, KIRYU, GUNMA, JAPAN |
| |
Abstract: | Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. In this article, we show two sufficient conditions for the existence of completely independent spanning trees. First, we show that a graph of n vertices has two completely independent spanning trees if the minimum degree of the graph is at least . Then, we prove that the square of a 2‐connected graph has two completely independent spanning trees. These conditions are known to be sufficient conditions for Hamiltonian graphs. |
| |
Keywords: | completely independent spanning trees Dirac's theorem Fleischner's theorem |
|
|