@article{Zhang2023, 
author = {Yixin Zhang and Yanbo Zhang and Hexuan Zhi},
title = {A proof of a conjecture on matching-path connected size Ramsey number},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {8027-8033},
keywords = {size Ramsey number, connected size Ramsey number, matching, path},
url = {https://www.sciopen.com/article/10.3934/math.2023406},
doi = {10.3934/math.2023406},
abstract = {For two graphs        G    1   and        G    2  , the connected size Ramsey number                                r          ^                      c    (      G    1    ,      G    2    ) is the smallest number of edges of a connected graph    G such that if each edge of    G is colored red or blue, then    G contains either a red copy of        G    1   or a blue copy of        G    2  . Let    n      K    2   be a matching with    n edges and        P    4   a path with four vertices. Rahadjeng, Baskoro, and Assiyatun [Procedia Comput. Sci. 74 (2015), 32-37] conjectured that                      r        ^                    c        (  n      K    2    ,      P    4    )  =  3  n  −  1 if    n is even, and                      r        ^                    c        (  n      K    2    ,      P    4    )  =  3  n otherwise. We verify the conjecture in this short paper.}
}