TY - JOUR
T1 - The size Ramsey and connected size Ramsey numbers for matchings versus paths
AU - Vito, V.
AU - Nabila, A. C.
AU - Safitri, E.
AU - Silaban, D. R.
N1 - Funding Information:
This work was financially supported by Universitas Indonesia under research grant PUTI with grant contract number NKB-942/UN2.RST/HKP.05.00/2020.
Publisher Copyright:
© 2021 Journal of Physics: Conference Series.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/1/12
Y1 - 2021/1/12
N2 - Given simple graphs F, G, and H, we write F → (G, H) if for every red-blue coloring of the edges of F, there exists either a red subgraph G or a blue subgraph H in F. The size Ramsey number for G and H, denoted by f (G,H), is the smallest size of a graph F which satisfies F → (G, H). If in addition F must be connected, then the resulting number is called the connected size Ramsey number for G and H, denoted by ȓc(G,H). In this paper, we obtain upper bounds for ȓ(tK2,Pm), ȓc(tK2,Pm), ȓ(tK2,P4 + a leaf), and ȓc(tK2,P4 + a leaf) for t ≥ 1 and m ≥ 3. We also determine the exact values of fc(2K2, Pm) and f(tK2, P3). In addition, the exact values of ȓc(tK2, P3) for t = 3,4 are given.
AB - Given simple graphs F, G, and H, we write F → (G, H) if for every red-blue coloring of the edges of F, there exists either a red subgraph G or a blue subgraph H in F. The size Ramsey number for G and H, denoted by f (G,H), is the smallest size of a graph F which satisfies F → (G, H). If in addition F must be connected, then the resulting number is called the connected size Ramsey number for G and H, denoted by ȓc(G,H). In this paper, we obtain upper bounds for ȓ(tK2,Pm), ȓc(tK2,Pm), ȓ(tK2,P4 + a leaf), and ȓc(tK2,P4 + a leaf) for t ≥ 1 and m ≥ 3. We also determine the exact values of fc(2K2, Pm) and f(tK2, P3). In addition, the exact values of ȓc(tK2, P3) for t = 3,4 are given.
KW - Connected size Ramsey number
KW - Matchings
KW - Paths
KW - Size Ramsey number
UR - http://www.scopus.com/inward/record.url?scp=85100714744&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/1725/1/012098
DO - 10.1088/1742-6596/1725/1/012098
M3 - Conference article
AN - SCOPUS:85100714744
SN - 1742-6588
VL - 1725
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012098
T2 - 2nd Basic and Applied Sciences Interdisciplinary Conference 2018, BASIC 2018
Y2 - 3 August 2018 through 4 August 2018
ER -