2025/06/23 by Cheng, Zhiyu, Luo, Zhidan, Chen, Pingge
#05C55 #05D10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.18235
Let H, H1 and H2 be graphs, and let H→ (H1, H2) denote that any red-blue coloring of E(H) yields a red copy of H1 or a blue copy of H2. The Ramsey number for H1 versus H2, r(H1, H2), is the minimum integer N such that KN→ (H1, H2). The Ramsey critical graph H for H1 versus H2 is a red-blue edge-colored KN- 1 such that H\not→ (H1, H2), where N= r(H1, H2). In this paper, we characterize all Ramsey critical graphs for a large tree versus tKm. As a corollary, we determine the star-critical Ramsey number for a large tree versus tKm.