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math.CO2025
Toughness in regular graphs from eigenvalues
Ruifang Liu, Ao Fan, Jinlong Shu
The {\it toughness} $τ(G)=\mathrm{min}\{\frac{|S|}{c(G-S)}: S~\mbox{is a vertex cut in}~G\}$ for which was initially proposed by Chvátal in 1973. A graph is call…
math.CO2025
On the Turán number of odd-ballooning of -chromatic graphs
Longfei Fang, Xueyi Huang, Huiqiu Lin +1
Given a graph , the Turán number is the maximum number of edges in any -vertex -free graph. The odd-ballooning of , denoted by , is a graph obtai…