2023/09/06 by He, Jialin, Hou, Xinmin, Ma, Jie +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2309.02993
In this paper, we investigate the minimum number of triangles, denoted by t(n,k), in n-vertex k-regular graphs, where n is an odd integer and k is an even integer. The well-known Andrásfai-Erdős-Sós Theorem has established that t(n,k)>0 if k>(2n)/(5). In a striking work, Lo has provided the exact value of t(n,k) for sufficiently large n, given that (2n)/(5)+(12√(n))/(5)