Hao Ying

Regular Graphs with Pairwise Distinct K_t-Degrees

For a fixed integer \(t \ge 3\), let \(\kappa_t(v)\) denote the number of copies of \(K_t\) containing a vertex \(v\). We prove that for every \(t \ge 6\) and every sufficiently large even integer \(r\), there exists an explicit connected \(r\)-regular graph on \(2r+2\) vertices...