Rainbow Pancyclicity in a Collection of Graphs Under the Dirac-type Condition  

作　　者：Lu-yi LI Ping LI Xue-liang LI 

机构地区：[1]Center for Combinatorics and LPMC,Nankai University,Tianjin 300071,China [2]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710062,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第2期269-274,共6页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.12131013,No.12161141006 and No.12201375);the Tianjin Research Innovation Project for Postgraduate Students(No.2022BKY039).

摘　　要：Let G={Gi:i∈[n]} be a collection of not necessarily distinct n-vertex graphs with the same vertex set V,where G can be seen as an edge-colored(multi)graph and each Gi is the set of edges with color i.A graph F on V is called rainbow if any two edges of F come from different Gis’.We say that G is rainbow pancyclic if there is a rainbow cycle Cℓof lengthℓin G for each integerℓ2[3,n].In 2020,Joos and Kim proved a rainbow version of Dirac’s theorem:Ifδ(Gi)≥2/n for each i∈[n],then there is a rainbow Hamiltonian cycle in G.In this paper,under the same condition,we show that G is rainbow pancyclic except that n is even and G consists of n copies of Kn/2,n/2.This result supports the famous meta-conjecture posed by Bondy.

关 键 词：RAINBOW Hamiltonian cycle rainbow pancyclic meta-conjecture 

分 类 号：O157.5[理学—数学]