Degree and neighborhood conditions for hamiltonicity of claw-free graphs

(ii) If k=3, δ(H)≥24, and for a given t (1≤t≤10) dt(H)>t(n+5)10, then H is Hamiltonian. These bounds on dt(H) in (i) and (ii) are sharp. It unifies and improves several prior results on conditions involved σt and Ut for the hamiltonicity of claw-free graphs. Since the number of graphs of orders at most max{4p−5,2p+1} are fixed for given p, improvements to (i) or (ii) by increasing the value of p are possible with the help of a computer.