Abstract
An edge-colored graph \(G\) is rainbow connected if every two vertices are connected by a path whose edges have distinct colors. It is known that deciding whether a given edge-colored graph is rainbow connected is NP-complete. We will prove that it is still NP-complete even when the edge-colored graph is a planar bipartite graph. A vertex-colored graph is rainbow vertex-connected if every two vertices are connected by a path whose internal vertices have distinct colors. It is known that deciding whether a given vertex-colored graph is rainbow vertex-connected is NP-complete. We will prove that it is still NP-complete even when the vertex-colored graph is a line graph.
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Supported by NSFC, “the Fundamental Research Funds for the Central Universities.”
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Communicated by Zhou Sanming.
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Huang, X., Li, X. & Shi, Y. Note on the Hardness of Rainbow Connections for Planar and Line Graphs. Bull. Malays. Math. Sci. Soc. 38, 1235–1241 (2015). https://doi.org/10.1007/s40840-014-0077-x
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DOI: https://doi.org/10.1007/s40840-014-0077-x