The \((\alpha ,\beta ,s,t)\)-diameter of graphs: a particular case of conditional diameter (Q2506366)

Given a property \(P\) of a pair \((G_1,G_2)\) of subgraphs of a graph \(G\), the conditional diameter or \(P\)-diameter measures the maximum distance among subgraphs satisfying \(P\). In this paper \(P\) requires that the minimum degrees of the subgraphs are at least \(\alpha\) and \(\beta\), and their orders are at least \(s\) and \(t\), respectively. Upper bounds on the conditional diameter are established by using alternating polynomials on the mesh of eigenvalues.