Abstract

The star-critical Ramsey number r∗(H1, H2) is the smallest integer k such that every red/blue coloring of the edges of Kn − K1,n−k−1 contains either a red copy of H1 or a blue copy of H2, where n is the graph Ramsey number R(H1, H2). We study the cases of r∗(C4, Cn) and R(C4, Wn). In particular, we prove that r∗(C4, Cn) = 5 for all n > 4, obtain a general characterization of Ramsey-critical (C4, Wn)-graphs, and establish the exact values of R(C4, Wn) for 9 cases of n between 18 and 44.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Publication Date

5-11-2015

Comments

Original article published in Discrete Applied Mathematics: doi:10.1016/j.dam.2015.01.003

Document Type

Article

Department, Program, or Center

Computer Science (GCCIS)

Campus

RIT – Main Campus

Available for download on Friday, May 11, 2018

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