Let G be a connected graph and let k be a positive 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 …

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 …

Abstract Graph Factors and Matching Extensions deals with two important branches of graph
theory-factor theory and extendable graphs. Due to the mature techniques and wide ranges …

A spanning k-tree of a connected graph G is a spanning tree in which each vertex admits
degree at most k. It is easy to see that a spanning 2-tree is a Hamiltonian path. Hence, a …

A k-tree is a spanning tree in which every vertex has degree at most k. In this paper, we
provide a sufficient condition for the existence of ak-tree in a connected graph with fixed …

Let k≥ 2 be an integer. A tree T is called ak-tree if d T (v)≤ k for each v∈ V (T); that is, the
maximum degree of ak-tree is at most k. A k-tree T is a spanning k-tree if T is a spanning …

We introduce the following combinatorial optimization problem: Given a connected graph G,
find a spanning tree T of G with the smallest number of branch vertices (vertices of degree 3 …

Let G be a graph of order n, and let a and b be integers such that 1≤ a< b. We show that G
has an a, b‐factor if δ (G)≥ a, n≥ 2a+ b+ a^2-ab and max dG (u), dG (v)≥ ana+b for any …