Anti-Ramsey Numbers in Complete k-Partite Graphs

Ding, Jili; Bian, Hong; Yu, Hui

doi:10.1155/2020/5136104

Cited by 4 publications

(2 citation statements)

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“…When replacing K n by other graph G, let ar(G, H) denote the maximum positive integer t such that there is a t-edge-colored G without any rainbow H. The researchers studied ar(G, kK 2 ) when G is a bipartite graph [5][6][7], complete split graph [8], hypergraph [9] and so on. For more results on anti-Ramsey numbers, we refer the readers to [10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

The Outer-Planar Anti-Ramsey Number of Matchings

et al. 2022

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A subgraph H of an edge-colored graph G is called rainbow if all of its edges have different colors. Let ar(G,H) denote the maximum positive integer t, such that there is a t-edge-colored graph G without any rainbow subgraph H. We denote by kK2 a matching of size k and On the class of all maximal outer-planar graphs on n vertices, respectively. The outer-planar anti-Ramsey number of graph H, denoted by ar(On,H), is defined as max{ar(On,H)|On∈On}. It seems nontrivial to determine the exact values for ar(On,H) because most maximal outer-planar graphs are asymmetry. In this paper, we obtain that ar(On,kK2)≤n+3k−8 for all n≥2k and k≥6, which improves the existing upper bound for ar(On,kK2), and prove that ar(On,kK2)=n+2k−5 for n=2k and k≥5. We also obtain that ar(On,6K2)=n+6 for all n≥29.

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Section: Introductionmentioning

confidence: 99%

The Outer-Planar Anti-Ramsey Number of Matchings

et al. 2022

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“…Fang, Győri, Li, and Xiao [31] studied C 3 and C 4 in complete r-partite graphs. Ding, Bian, and Yu [22] found anti-Ramsey numbers for spanning trees, Hamiltonian cycles, and perfect matchings in r-partite graphs. The value of ar(K n 1 ,...,n k , K ℓ ) is given in [6].…”

Section: Multipartite Graphsmentioning

confidence: 99%