On the Maximum Degree of $3_t$-Critical Graphs

Abstract

We give general lower bounds and upper bounds on the maximum degree $\mathrm{\Delta }(G)$ of a $3_t$-critical graph $G$ in terms of the order of $G$. We also establish tighter sharp lower bounds on $\mathrm{\Delta }(G)$ in terms of the order of $G$ for several families of $3_t$-critical graphs, such as crown-graphs, claw-free graphs, and graphs with independence number $\alpha (G)=2$.