An exact Ramsey number of large bipartite graphs versus odd wheel

2025/11/18 by Gupta, Sayan, Majumder, Kaushik
#05D10 #05D40. Secondary: 05C35 #Combinatorics (math.CO) #FOS: Mathematics #Primary: 05C55

paper · doi:10.48550/arxiv.2511.14867

Abstract

The Ramsey number for the pair of graphs \mathbbK_1,n (star) versus W_m (wheel) has been extensively studied. In contrast, the Ramsey number of \mathbbK_2,n versus wheel is not yet explored due to the structural complexity of \mathbbK_2,n. In this article, we have established an exact value of \mathbbK_2,n versus W_m for large n and m. In particular, we have proved R(\mathbbK_2,n, W_m)=3n+4 if n and m are sufficiently large integers where n≥4m and m is an odd integer. This also proves the W_m-goodness of \mathbbK_2,n. We have used a probabilistic method composed of structural analysis in our proof.

Citations

• A study of two Ramsey numbers involving odd cycles
• The Ramsey number of a long even cycle versus a star
• Ramsey goodness of cycles
• On star-wheel Ramsey numbers
• Ramsey-goodness -- and otherwise
• Ramsey Goodness and Beyond

Related

• On star-wheel Ramsey numbers
• A note on the Ramsey number of even wheels versus stars
• The Ramsey Number for Tree Versus Wheel with Odd Order
• The Ramsey numbers for trees of order n with maximum degree at least n-5 versus the wheel graph of order nine
• Ramsey numbers of trees versus odd cycles