Localized Conditions with d_L{(x,y)}2 for R Hamiltonian Graphs
Feng Liu · Journal of Henan Normal University · 2003
For an integer i and an induced subgraph L of graph G, if x,y∈V(L),d L(x,y)=imax{d G(x),d G(y)}|G|/2,then L is called possessing the property D L(i). Let C(G) be the closure of the graph G. The following result is obtained in this paper: For any 2-connected graph with C(G)=G and λ(G)3, if there exists an integer s such that each induced subgraph L satisfying: (i) L possesses D L(2) if LK 1.3; (ii) For any integer i,1is,L possesses D L(i) if LB i; (iii) L possesses D L(s+2) if LZ s+2, then G is hamiltonian. As a by-product, we get that every 2-connected {K 1.3;B i,11s}-free graph with C(G)=G,λ(G)3 and max{d G(x),d G(y)| For any induced subgraph LZ s+2, d L(x,y)=s+2|G|/2 is hamiltonian.