MINIMAL HYPER-HAMILTON LACEABLE GRAPHS

A Hamilton laceable graph G on n nodes is defined to be hyper-Hamilton laceable if either (1) G is equitable and if v is any node of G, G - v is Hamilton laceable, or (2) G is nearly equitable and if v is any n ode in the larger color set, G - v is Hamilton laceable. The minimum n umber of edges needed for G to be hyper-Hamilton laceable in the case where n = 2k > 4 is shown to be 3k. In the case where n = 2k + 1 > 3, the minimum number of edges, E(n), is shown to satisfy the inequality 3k less-than-or-equal-to E(n) less-than-or-equal-to 4k - 1.