Circumference, Minimum Degree and Clique Number - Yuan, Long-Tu (The Electronic Journal of Combinatorics, 2024)
The circumference and the clique number of a graph is the length of a longest cycle and the largest order of a clique in it respectively. We show that the circumference of a 2-connected non-Hamiltonian graph G is at least the sum of its clique number and minimum degree unless G is one of two specific graphs.