Showing papers on "K-tree published in 2019"
TL;DR: This paper proves that κ ( G c ) = δ (G c ) .
2 citations
TL;DR: A k-tree is a tree with maximum degree at most k for a graph G and u,v ∈ V (G) with uv∉E(G), let α(u,v; G) be the cardinality of a maximum independent set containing u and v.
Abstract: A k-tree is a tree with maximum degree at most k. For a graph G and u,v ∈ V (G) with uv∉E(G), let α(u,v; G) be the cardinality of a maximum independent set containing u and v. For a graph G and u,v...
TL;DR: In this article, the minimum value of the degree sum of k independent vertices in a graph G is given, where G is an (s + 1)-connected graph with σk(G) ≥∣G∣ + (k − t)s − 1.
Abstract: A k-tree is a tree with maximum degree at most k. In this paper, we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t, where 1 ≤ t ≤ k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 2, s ≥ 0 and 1 ≤ t ≤ k be integers, and suppose G is an (s + 1)-connected graph with σk(G) ≥∣G∣ + (k − t)s − 1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree at most t. This improves a result obtained by Matsuda and Matsumura.