Anti-Ramsey numbers for vertex-disjoint triangles

Fangfang Wu; Shenggui Zhang; Binlong Li; Jimeng Xiao

doi:10.1016/j.disc.2022.113123

Anti-Ramsey numbers for vertex-disjoint triangles

Fangfang Wu
, Shenggui Zhang
, Binlong Li
, Jimeng Xiao

School of Mathematics and Statistics

Northwestern Polytechnical University Xian

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

An edge-colored graph is called rainbow if all the colors on its edges are distinct. Given a positive integer n and a graph G, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of K_n with no rainbow copy of G. Denote by kC₃ the union of k vertex-disjoint copies of C₃. In this paper, we determine the anti-Ramsey number ar(n,kC₃) for n=3k and n≥2k²−k+2, respectively. When 3k≤n≤2k²−k+2, we give lower and upper bounds for ar(n,kC₃).

Original language	English
Article number	113123
Journal	Discrete Mathematics
Volume	346
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2022.113123
State	Published - Jan 2023

Keywords

Anti-Ramsey number
Complete graphs
Vertex-disjoint triangles

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10.1016/j.disc.2022.113123

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title = "Anti-Ramsey numbers for vertex-disjoint triangles",

abstract = "An edge-colored graph is called rainbow if all the colors on its edges are distinct. Given a positive integer n and a graph G, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of G. Denote by kC3 the union of k vertex-disjoint copies of C3. In this paper, we determine the anti-Ramsey number ar(n,kC3) for n=3k and n≥2k2−k+2, respectively. When 3k≤n≤2k2−k+2, we give lower and upper bounds for ar(n,kC3).",

keywords = "Anti-Ramsey number, Complete graphs, Vertex-disjoint triangles",

author = "Fangfang Wu and Shenggui Zhang and Binlong Li and Jimeng Xiao",

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year = "2023",

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doi = "10.1016/j.disc.2022.113123",

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T1 - Anti-Ramsey numbers for vertex-disjoint triangles

AU - Wu, Fangfang

AU - Zhang, Shenggui

AU - Li, Binlong

AU - Xiao, Jimeng

PY - 2023/1

Y1 - 2023/1

N2 - An edge-colored graph is called rainbow if all the colors on its edges are distinct. Given a positive integer n and a graph G, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of G. Denote by kC3 the union of k vertex-disjoint copies of C3. In this paper, we determine the anti-Ramsey number ar(n,kC3) for n=3k and n≥2k2−k+2, respectively. When 3k≤n≤2k2−k+2, we give lower and upper bounds for ar(n,kC3).

AB - An edge-colored graph is called rainbow if all the colors on its edges are distinct. Given a positive integer n and a graph G, the anti-Ramsey number ar(n,G) is the maximum number of colors in an edge-coloring of Kn with no rainbow copy of G. Denote by kC3 the union of k vertex-disjoint copies of C3. In this paper, we determine the anti-Ramsey number ar(n,kC3) for n=3k and n≥2k2−k+2, respectively. When 3k≤n≤2k2−k+2, we give lower and upper bounds for ar(n,kC3).

KW - Anti-Ramsey number

KW - Complete graphs

KW - Vertex-disjoint triangles

UR - https://www.scopus.com/pages/publications/85136074470

U2 - 10.1016/j.disc.2022.113123

DO - 10.1016/j.disc.2022.113123

M3 - 文章

AN - SCOPUS:85136074470

SN - 0012-365X

VL - 346

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

M1 - 113123

ER -

Anti-Ramsey numbers for vertex-disjoint triangles

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