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【期刊论文】Hamiltonian cycles in 3-connected Claw-free graphs
李国君, Guojun Lia, *, , M. Lub, Z. Liuc
Discrete Mathematics 250(2002)137-151,-0001,():
-1年11月30日
It is shown that every 3-connected claw-free graph having at most 6δ-7 vertices is hamiltonian, where is the minimum degree.
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【期刊论文】Orthogonal factorizations of graphs
李国君, GuojunLia, *, Chuanping Chenb, Gang Yuc,
Discrete Mathematics 245(2002)173-194,-0001,():
-1年11月30日
Let G be a graph with vertex set V(G) and edge set E(G); and let g and f be two nonnegative integer-valued functions de3ned on V(G) such that g(x)≤(x) for every vertex x of V(G). We use dG(x) to denote the degree of a vertex x of G. A graph G is called a (g; f)-graph if g(x) ≤G(x) ≤(x) for each x ∈ V(G). Then a spanning subgraph F of G is said to be a (g; f)-factor of G if F itself is a (g; f)-graph. A (g; f)-factorizationof G is a partitionof E(G) into edge disjoint (g; f)-factors. Let F={F1; F2; : : : ; Fm} be a factorizationof G and H be a subgraph of G with m edges. If Fi≤i≤m, has exactly one edge in common with H, we say that F is orthogonal to H. Inthis paper it is proved that every (mg + k;mf − k)-graph contains a subgraph R such that R has a (g; f)-factorizationorthogon al to a givensubgraph with k edges, where m and k are positive integers with 1≤k<m and g(x)≥0. This result has been conjectured by YaninYan(Sci. China Ser. A 41(1) (1998) 48).
Integer-valued functions, Spanning subgraph, (, g,, f), -factor, Orthogonal factorization
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