2020
DOI: 10.48550/arxiv.2006.06551
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Upper Bounding Rainbow Connection Number by Forest Number

Abstract: A path in an edge-colored graph is rainbow if no two edges of it are colored the same, and the graph is rainbow-connected if there is a rainbow path between each pair of its vertices. The minimum number of colors needed to rainbow-connect a graph G is the rainbow connection number of G, denoted by rc(G).A simple way to rainbow-connect a graph G is to color the edges of a spanning tree with distinct colors and then re-use any of these colors to color the remaining edges of G. This proves that rc(G) ≤ |V (G)| − … Show more

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