Given a graph G and a positive integer k, define the Gallai-Ramsey number to be the minimum number of vertices n such that any k-edge coloring of Kn\documentclass[12pt]{minimal}
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\begin{document}$$K_n$$\end{document} contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this paper, we consider two classes of unicyclic graphs, the star with an extra edge and the path with a triangle at one end. We provide the 2-color Ramsey numbers for these two classes of graphs and use these to obtain general upper and lower bounds on the Gallai-Ramsey numbers.
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China Jiliang Univ, Coll Sci, Hangzhou 310018, Peoples R ChinaChina Jiliang Univ, Coll Sci, Hangzhou 310018, Peoples R China
Wang, Zhao
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Mao, Yaping
Magnant, Colton
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Acad Plateau Sci & Sustainabil, Xining 810008, Qinghai, Peoples R China
United Parcel Serv, Adv Analyt Grp, Atlanta, GA USAChina Jiliang Univ, Coll Sci, Hangzhou 310018, Peoples R China
Magnant, Colton
Zou, Jinyu
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Qinghai Univ, Dept Basic Course, Xining 810016, Peoples R ChinaChina Jiliang Univ, Coll Sci, Hangzhou 310018, Peoples R China
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China Jiliang Univ, Coll Sci, Hangzhou 310018, Peoples R ChinaQinghai Normal Univ, Sch Math & Stat, Xining 810008, Qinghai, Peoples R China
Wang, Zhao
Magnant, Colton
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Acad Plateau Sci & Sustainabil, Xining 810008, Qinghai, Peoples R China
UPS Amer Inc, Atlanta, GA 30328 USAQinghai Normal Univ, Sch Math & Stat, Xining 810008, Qinghai, Peoples R China
Magnant, Colton
Schiermeyer, Ingo
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Tech Univ Bergakad Freiberg, Inst Diskrete Math & Algebra, D-09596 Freiberg, GermanyQinghai Normal Univ, Sch Math & Stat, Xining 810008, Qinghai, Peoples R China
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Qinghai Normal Univ, Sch Comp, Xining 810008, Qinghai, Peoples R China
Qinghai Univ, Dept Basic Res, Xining 810008, Qinghai, Peoples R ChinaQinghai Normal Univ, Sch Comp, Xining 810008, Qinghai, Peoples R China
Zou, Jinyu
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Mao, Yaping
Magnant, Colton
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Clayton State Univ, Dept Math, Morrow, GA 30260 USA
Acad Plateau Sci & Sustainabil, Xining 810008, Qinghai, Peoples R ChinaQinghai Normal Univ, Sch Comp, Xining 810008, Qinghai, Peoples R China
Magnant, Colton
Wang, Zhao
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China Jiliang Univ, Coll Sci, Hangzhou 310018, Zhejiang, Peoples R ChinaQinghai Normal Univ, Sch Comp, Xining 810008, Qinghai, Peoples R China
Wang, Zhao
Ye, Chengfu
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Qinghai Normal Univ, Sch Comp, Xining 810008, Qinghai, Peoples R ChinaQinghai Normal Univ, Sch Comp, Xining 810008, Qinghai, Peoples R China
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Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaNorthwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
Su, Xueli
Liu, Yan
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South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R ChinaNorthwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
机构:Qinghai Normal Univ, Sch Math & Stat, Xining 810008, Qinghai, Peoples R China
Zhou, Jiannan
Li, Zhihui
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机构:Qinghai Normal Univ, Sch Math & Stat, Xining 810008, Qinghai, Peoples R China
Li, Zhihui
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Mao, Yaping
Wei, Meiqin
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Shaanxi Normal Univ, Sch Math & Stat, Xian 710062, Shaanxi, Peoples R China
Shanghai Maritime Univ, Coll Arts & Sci, Shanghai 201306, Peoples R ChinaQinghai Normal Univ, Sch Math & Stat, Xining 810008, Qinghai, Peoples R China
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Clayton State Univ, Dept Math, Morrow, GA 30260 USANorthwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
Besse, Pierre
Magnant, Colton
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Clayton State Univ, Dept Math, Morrow, GA 30260 USA
Acad Plateau Sci & Sustainabil, Xining 810008, Qinghai, Peoples R ChinaNorthwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
Magnant, Colton
Wang, Ligong
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Northwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
Northwestern Polytech Univ, Xian Budapest Joint Res Ctr Combinator, Xian 710129, Shaanxi, Peoples R ChinaNorthwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China
Wang, Ligong
Watts, Noah
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Clayton State Univ, Dept Math, Morrow, GA 30260 USANorthwestern Polytech Univ, Sch Math & Stat, Xian 710129, Shaanxi, Peoples R China