Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or Ḡ contains a G2. Parsons gave a recursive formula to determine the values of R(Pn,K1,m), where Pn is a path on n vertices and K1,m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(Pn,K1,m), where Pn is a linear forest on m vertices. We determine the exact values of R(Pn,K1∨Fm) for the cases m ≤ n and m ≥ 2n, and for the case that Fm has no odd component. Moreover, we give a lower bound and an upper bound for the case n+1 ≤ m ≤ 2n−1 and Fm has at least one odd component.
@article{bwmeta1.element.doi-10_1515_umcsmath-2015-0002,
author = {Binlong Li and Bo Ning},
title = {On path-quasar Ramsey numbers},
journal = {Annales UMCS, Mathematica},
volume = {68},
year = {2015},
zbl = {1308.05077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0002}
}
Binlong Li; Bo Ning. On path-quasar Ramsey numbers. Annales UMCS, Mathematica, Tome 68 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_umcsmath-2015-0002/
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