Spanning trees with small degrees and few leaves

TL;DR

This paper establishes an Ore-type condition that guarantees the existence of a spanning tree in a graph with limited degrees and a small number of leaves, contributing to graph theory and network design.

Contribution

It introduces a new Ore-type criterion that ensures graphs contain spanning trees with constrained degrees and leaves, advancing theoretical understanding.

Findings

Provides a sufficient Ore-type condition for such spanning trees

Characterizes the degree and leaf constraints in spanning trees

Enhances methods for constructing efficient network topologies

Abstract

We give an Ore-type condition sufficient for a graph G to have a spanning tree with small degrees and with few leaves.