A K_(1,3)-free Hamiltonian Graphs
Zhao Ke · 2007
In 1998 a conjecture was suggested for the conference of Graph theory,combinatorics,and applications at Kalamazooin USA as follows:let G be a 3-connected K1,3-free graph of order n,if |N(x)∪N(y)|≥(2n-6)/3 for each pair of nonadjacent vertices x,y,then G is Hamiltonian.In this note we obtain the further result:let G be a 3-connected K1,3-free grah of order n,if |N(x)∪N(y)|≥(2n-6)/3 for each pair of nonadjacent vertices x,y with 1≤|N(x)∩N(y)|≤α-1,then G is Hamiltonian.