Electronic Theses and Dissertations

Date of Award


Document Type


Degree Name

Ph.D. in Mathematics



First Advisor

Bing Wei

Second Advisor

Haidong Wu

Third Advisor

Talmage James Reid

Relational Format



In 1930, Frank Ramsey showed that one will find a monochromatic clique of a specified size in any edge coloring of a sufficiently large complete graph. This result is commonly known as Ramsey's theorem. The role of Ramsey number is to quantify some specific problems related to Ramsey's theorem. Given a graph H, the Ramsey number R_2(H) is the minimum integer p such that every 2-edge-coloring of the complete graph K_p contains a monochromatic copy of H. Ramsey numbers have been a hot topic in graph theory for decades due to their intrinsic beauty, wide applicability and overwhelming difficulty. Let F_n be a graph consisting of n triangles, all sharing one common vertex, and S_{t,r} (r\ge2) be a graph obtained from a star with t vertices by adding a path P_r which connects r distinct leaves of the star. Chen, Yu and Zhao (2021) speculated that R_2(F_n)\le R_2(nK_3)=5n for some n\ge2. However, the exact value for R_2(F_n) is very hard to determine. So far, it has been verified for n=2. We confirm their assertion for n=3 by proving that R_2(F_3)=14. We also study the Ramsey numbers of S_{t,r} and obtain the exact values of R_2(S_{t,r}) for 2\le r\le4.

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