Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let G be a claw-free graph and let cl(G) be the closure of G.  present a method for characterizing classes Gi, i = 3,..., 7, of 2-connected closed claw-free graphs with the following properties. (i) Theorem. Let G be a 2-connected claw-free graph of order n ≥ 153 such that δ(G) ≥ 20 and σ8(G) > n + 39. Then either G is hamiltonian or cl (G) ∈ ∪i=37 Gi. (ii) Corollary. Let G be a 2-connected claw-free graph of order n ≥ 153 with δ(G) ≥ (n + 39)/8. Then either G is hamiltonian or cl (G) ∈ ∪i=37 Gi.The family of exceptions contains 318 infinite classes. The majority of these exception classes re found with the help of a computer.
['Ondrej Kovárík', 'Milos Mulac', 'Zdenek Ryjácek']
I am writing a research paper on a idea A note on degree conditions for Hamiltonicity in 2-connected claw-free graphs
[{"from": "human", "value": "I am writing a research paper on a idea A note on degree conditions for Hamiltonicity in 2-connected claw-free graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let G be a claw-free graph and let cl(G) be the closure of G.  present a method for characterizing classes Gi, i = 3,..., 7, of 2-connected closed claw-free graphs with the following properties. (i) Theorem. Let G be a 2-connected claw-free graph of order n \u2265 153 such that \u03b4(G) \u2265 20 and \u03c38(G) > n + 39. Then either G is hamiltonian or cl (G) \u2208 \u222ai=37 Gi. (ii) Corollary. Let G be a 2-connected claw-free graph of order n \u2265 153 with \u03b4(G) \u2265 (n + 39)/8. Then either G is hamiltonian or cl (G) \u2208 \u222ai=37 Gi.The family of exceptions contains 318 infinite classes. The majority of these exception classes re found with the help of a computer."}]