2

2

3455

[a, b]-Factors Excluding Some Specified Edges In Graphs

Let G be a graph of order n, and let a, b and m be positive integers with 1 ≤ a<b. An [a, b]-factor of G is deﬁned as a spanning subgraph F of G such that a ≤ dF (x) ≤ b for each x ∈ V (G). In this paper, it is proved that if n ≥ (a+b−1+√(a+b+1)m−2)2−1 b and δ(G) > n + a + b − 2 √bn+ 1, then for any subgraph H of G with m edges, G has an [a, b]-factor F such that E(H)∩ E(F) = ∅. This result is an extension of thatof Egawa [2].

graph, minimum degree, [a, b]-factor.

1

8232

Hamiltonian Factors in Hamiltonian Graphs

Let G be a Hamiltonian graph. A factor F of G is called
a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper,
two sufficient conditions are given, which are two neighborhood
conditions for a Hamiltonian graph G to have a Hamiltonian factor.

graph, neighborhood, factor, Hamiltonian factor.