2023/10/17 by Wang, Junjie, Hou, Yaoping, Huang, Xueyi · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2310.11061
In this paper, we study the Turán problem for C2k+1-. Suppose that G is an unbalanced signed graph of order n with e(G) edges. Let λ1 (G) be the largest eigenvalue of G, and C2k+1- be the set of the negative cycle with length 2k+1(3 ≤ k ≤ (n)/(15)). We prove that if G is a C2k+1--free unbalanced signed graph, then e(G) ≤ e(C3- ⋅ Kn-2) and λ1(G) ≤ λ1(C3- ⋅ Kn-2), with equality holding if and only if G is switching equivalent to C3- ⋅ Kn-2.