Balanced Spanning Caterpillars

TL;DR

This paper establishes a precise minimum degree condition under which a graph contains a spanning p-caterpillar, a specific type of caterpillar with balanced leaf distribution.

Contribution

It provides a tight characterization of the minimum degree needed for a graph to contain a spanning p-caterpillar, advancing understanding of graph spanning structures.

Findings

Derived a tight minimum degree threshold for spanning p-caterpillars.

Characterized the structure of graphs that contain such caterpillars.

Extended the theory of spanning trees with balanced leaf distributions.

Abstract

A $p$-caterpillar is a caterpillar such that every non-leaf vertex is adjacent to exactly $p$ leaves. We give a tight minimum degree condition for a graph to have a spanning $p$-caterpillar.