| Autor: |
Chartrand Gary, Devereaux Stephen, Haynes Teresa W., Hedetniemi Stephen T., Zhang Ping |
| Jazyk: |
angličtina |
| Rok vydání: |
2018 |
| Předmět: |
|
| Zdroj: |
Discussiones Mathematicae Graph Theory, Vol 38, Iss 4, Pp 1007-1021 (2018) |
| Druh dokumentu: |
article |
| ISSN: |
2083-5892 |
| DOI: |
10.7151/dmgt.2061 |
| Popis: |
Let G be a nontrivial connected, edge-colored graph. An edge-cut R of G is called a rainbow cut if no two edges in R are colored the same. An edge-coloring of G is a rainbow disconnection coloring if for every two distinct vertices u and v of G, there exists a rainbow cut in G, where u and v belong to different components of G − R. We introduce and study the rainbow disconnection number rd(G) of G, which is defined as the minimum number of colors required of a rainbow disconnection coloring of G. It is shown that the rainbow disconnection number of a nontrivial connected graph G equals the maximum rainbow disconnection number among the blocks of G. It is also shown that for a nontrivial connected graph G of order n, rd(G) = n−1 if and only if G contains at least two vertices of degree n − 1. The rainbow disconnection numbers of all grids Pm _ Pn are determined. Furthermore, it is shown for integers k and n with 1 ≤ k ≤ n − 1 that the minimum size of a connected graph of order n having rainbow disconnection number k is n + k − 2. Other results and a conjecture are also presented. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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