Rainbow Connection Number of Graphs with Diameter 3
A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every pair of distinct vertices of G is connected by a rainbow path. Let f(d) deno...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2017-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1920 |
| Summary: | A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every pair of distinct vertices of G is connected by a rainbow path. Let f(d) denote the minimum number such that rc(G) ≤ f(d) for each bridgeless graph G with diameter d. In this paper, we shall show that 7 ≤ f(3) ≤ 9. |
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| ISSN: | 2083-5892 |