On the Maximum Degree of \(3_{t}\)-Critical Graphs

We give general lower bounds and upper bounds on the maximum degree \(\Delta(G)\) of a \(3_t\)-critical graph \(G\) in terms of the order of \(G\). We also establish tighter sharp lower bounds on \(\Delta(G)\) 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 \(\alpha(G) = 2\).