@inbook{ac7fa15891fb406292d7e2c2d8a44358,

title = "The Ramsey Numbers of Paths Versus Fans",

abstract = "For two given graphs G and H, the Ramsey number R(G,H) is the smallest positive integer p such that for every graph F on p vertices the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Fm), where Pn is a path on n vertices and Fm is the graph obtained from m disjoint triangles by identifying precisely one vertex of every triangle (Fm is the join of K1 and mK2). We determine exact values for R(Pn,Fm) for the following values of n and m: n = 1,2 or 3 and m ≥ 2; n ≥ 4 and 2 ≤ m ≤ (n + 1)/2; n ≥ 7 and m = n − 1 or m = n; n ≥ 8 and (k · n − 2k + 1)/2 ≤ m ≤ (k · n − k + 2)/2 with 3 ≤ k ≤ n − 5; n = 4,5 or 6 and m ≥ n − 1; n ≥ 7 and m ≥ (n − 3)2/2.",

keywords = "Path, IR-74946, Fan, Ramsey number",

author = "M. Salman",

year = "2003",

doi = "10.1016/S1571-0653(04)00448-2",

language = "Undefined",

series = "Electronic Notes in Discrete Mathematics",

publisher = "Elsevier",

pages = "103--107",

editor = "Broersma, {Haitze J.} and U. Faigle and Hurink, {Johann L.} and Stefan Pickl and Gerhard Woeginger",

booktitle = "2nd Cologne-Twente Workshop on Graphs and Combinatorial Optimization",

address = "Netherlands",

note = "2nd Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2003 ; Conference date: 14-05-2003 Through 16-05-2003",

}