TY - JOUR
T1 - Gallai–Ramsey Numbers for a Class of Graphs with Five Vertices
AU - Li, Xihe
AU - Wang, Ligong
N1 - Publisher Copyright:
© 2020, Springer Japan KK, part of Springer Nature.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - Given two graphs G and H, the k-colored Gallai–Ramsey number grk(G: H) is defined to be the minimum integer n such that every k-coloring of the complete graph on n vertices contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we consider grk(K3: H) , where H is a connected graph with five vertices and at most six edges. There are in total thirteen graphs in this graph class, and the Gallai–Ramsey numbers for eight of them have been studied step by step in several papers. We determine all the Gallai–Ramsey numbers for the remaining five graphs, and we also obtain some related results for a class of unicyclic graphs. As applications, we find the mixed Ramsey spectra S(n; H, K3) for these graphs by using the Gallai–Ramsey numbers.
AB - Given two graphs G and H, the k-colored Gallai–Ramsey number grk(G: H) is defined to be the minimum integer n such that every k-coloring of the complete graph on n vertices contains either a rainbow copy of G or a monochromatic copy of H. In this paper, we consider grk(K3: H) , where H is a connected graph with five vertices and at most six edges. There are in total thirteen graphs in this graph class, and the Gallai–Ramsey numbers for eight of them have been studied step by step in several papers. We determine all the Gallai–Ramsey numbers for the remaining five graphs, and we also obtain some related results for a class of unicyclic graphs. As applications, we find the mixed Ramsey spectra S(n; H, K3) for these graphs by using the Gallai–Ramsey numbers.
KW - Gallai–Ramsey number
KW - Mixed Ramsey spectrum
KW - Rainbow triangle
UR - http://www.scopus.com/inward/record.url?scp=85085898557&partnerID=8YFLogxK
U2 - 10.1007/s00373-020-02194-5
DO - 10.1007/s00373-020-02194-5
M3 - 文章
AN - SCOPUS:85085898557
SN - 0911-0119
VL - 36
SP - 1603
EP - 1618
JO - Graphs and Combinatorics
JF - Graphs and Combinatorics
IS - 6
ER -