This book chronicles the development of graph factors and factorizations. It pursues a
comprehensive approach, addressing most of the important results from hundreds of …

In this paper, we give a survey of spanning trees. We mainly deal with spanning trees having
some particular properties concerning a hamiltonian properties, for example, spanning trees …

Let G be a connected graph and let k≥ 1 be an integer. Let T be a spanning tree of G. The
leaf degree of a vertex v∈ V (T) is defined as the number of leaves adjacent to v in T. The …

Degree Conditions for the Existence of Vertex-Disjoint Cycles and Paths: A Survey |
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For any integer k≥ 2, a spanning k-ended-tree is a spanning tree with at most k leaves.
Motivated by the degree sum condition of Broersma and Tuinstra (1998)[4], we provide tight …

For a graph H and an integer k≥ 2, let σk (H) denote the minimum degree sum of k
independent vertices of H. We prove that if a connected claw-free graph G satisfies σk+ 1 …

A factor of a graph is a spanning subgraph satisfying some given conditions. An earlier
survey of factors can be traced back to the Akiyama and Kano [J. Graph Theory, 1985, 9: 1 …

Let k be a non-negative integer. A branch vertex of a tree is a vertex of degree at least three.
We show two sufficient conditions for a connected claw-free graph to have a spanning tree …

In 2009, Kyaw proved that every n-vertex connected K 1, 4-free graph G with σ 4 (G)≥ n− 1
contains a spanning tree with at most 3 leaves. In this paper, we prove an analogue of …

A tree with atmost m leaves is called an m-ended tree. Kyaw proved that every connected K
1, 4-free graph with σ 4 (G)⩽ n− 1 contains a spanning 3-ended tree. In this paper we obtain …