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- W2980821823 abstract "For an edge-colored graph, a subgraph is called rainbow if all its edges have distinct colors. We show that if G is an edge-colored graph of order n and size m using c colors on its edges, and m+c≥n+12+k−1 for a non-negative integer k, then G contains at least k rainbow triangles. For n≥3k, we show that this result is best possible, and we completely characterize the class of edge-colored graphs for which this result is sharp. Furthermore, we show that an edge-colored graph G contains at least k rainbow triangles if ∑v∈V(G)dGc(v)≥n+12+k−1 where dGc(v) denotes the number of distinct colors incident to a vertex v. Finally we characterize the edge-colored graphs without a rainbow clique of size at least six that maximizes the sum of edges and colors m+c. Our results answer two questions of Fujita et al., 2019." @default.
- W2980821823 created "2019-10-25" @default.
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- W2980821823 date "2020-02-01" @default.
- W2980821823 modified "2023-09-27" @default.
- W2980821823 title "Rainbow triangles and cliques in edge-colored graphs" @default.
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- W2980821823 doi "https://doi.org/10.1016/j.ejc.2019.103037" @default.
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