Zhaohong Niu

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Let G be a connected simple graph of order n, k a positive integer and n sufficiently large relative to k. An even factor of G is a spanning subgraph of G in which every vertex has even positive degree. In this paper, we prove that if δ(G) ≥ n/k − 1, then the (collapsible) reduction G′ of G satisfies |V (G′)| ≤ k, and the preimage of each vertex of G′ is(More)
A graph is k-supereulerian if it has a spanning even subgraph with at most k components. We show that if G is a connected graph and G is the (collapsible) reduction of G, then G is k-supereulerian if and only if G is k-supereulerian. This extends Catlin’s reduction theorem in [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph(More)
A graph G is called k-supereulerian if it has a spanning even subgraph with at most k components. In this paper, we prove that any 2-edge-connected loopless graph of order n is ⌈(n − 2)/3⌉-supereulerian, with only one exception. This result solves a conjecture in [Z. Niu, L. Xiong, Even factor of a graphwith a bounded number of components, Australas. J.(More)
Let G be a simple graph of order n and D1(G) be the set of vertices of degree 1 in G. In this paper, we prove that if G − D1(G) is 2-edge-connected and if for every edge xy ∈ E(G), max{d(x), d(y)} ≥ n/6 − 1, then for n large, L(G) is traceable with the exception of a class of well characterized graphs. A similar result in (Lai, Discrete Math 178:93–107,(More)
A graph G has the hourglass property if every induced hourglass S (a tree with a degree sequence 22224) contains two non-adjacent vertices which have a common neighbor in G − V (S). For an integer k ≥ 4, a graph G has the single k-cycle property if every edge of G, which does not lie in a triangle, lies in a cycle C of order at most k such that C has at(More)
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