# On the Extremal Number of Edges in Hamiltonian Graphs

Tung-Yang Ho*, Cheng-Kuan Lin, Jiann-Mean Tan, D. Frank Hsu, Lih Hsing Hsu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

## Abstract

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.
Original language English 1659-1665 Journal of Information Science and Engineering 27 5 https://doi.org/10.6688/JISE.2011.27.5.9 Published - Sep 2011

## Keywords

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