On the Extremal Number of Edges in Hamiltonian Graphs

作者：Ho Tung Yang^*; Lin Cheng Kuan; Tan Jimmy J M; Hsu D Frank; Hsu Lih Hsing

来源：Journal of Information Science and Engineering, 2011, 27(5): 1659-1665.

• complete graph
• cycle
• hamiltonian
• hamiltonian cycle
• edge-fault tolerant hamiltonian

Assume that n and delta are positive integers with 2 <= delta < n. Let h(n, delta) be the minimum number of edges required to guarantee an n-vertex graph with minimum degree delta(G) >= delta be hamiltonian, i.e., any n-vertex graph G with delta(G) >= delta is hamiltonian if vertical bar E(G)vertical bar >= h(n, delta).
We move that h(n, delta) = (n - delta, 2) + delta(2) +1 if delta <= left perpendicular n + 1 + x ((n + 1mld 2)/6 right perpendicular, h(n, delta) = C(n - left perpendicular n - 1/2 right perpendicular, 2) + left perpendicular n - 1/2 right perpendicular(2) + 1 if left perpendicular n + 1 + 3 x ((n + 1) mod2)/6 < delta <= left perpendicular n - 1/2 right perpendicular, and h(n, delta, = inverted right perpendicular n delta/2inverted left perpendicular if delta > left perpendicular n - 1/2 right perpendicular.

• 出版日期2011-9