Displaying similar documents to “Functions on adjacent vertex degrees of trees with given degree sequence”

On a Spanning k-Tree in which Specified Vertices Have Degree Less Than k

Hajime Matsumura (2015)

Discussiones Mathematicae Graph Theory

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A k-tree is a tree with maximum degree at most k. In this paper, we give a degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than k. We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G. Let k ≥ 3 and s ≥ 0 be integers, and suppose G is a connected graph and σk(G) ≥ |V (G)|+s−1. Then for any s specified vertices, G contains a spanning k-tree in which every specified vertex has degree less than...

Completely Independent Spanning Trees in (Partial) k-Trees

Masayoshi Matsushita, Yota Otachi, Toru Araki (2015)

Discussiones Mathematicae Graph Theory

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Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that [k/2] ≤ cist(G) ≤ k − 1 for any k-tree G. Then we show that for any p ∈ {[k/2], . . . , k − 1}, there exist infinitely many k-trees G such...

Characterization Results for theL(2, 1, 1)-Labeling Problem on Trees

Xiaoling Zhang, Kecai Deng (2017)

Discussiones Mathematicae Graph Theory

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An L(2, 1, 1)-labeling of a graph G is an assignment of non-negative integers (labels) to the vertices of G such that adjacent vertices receive labels with difference at least 2, and vertices at distance 2 or 3 receive distinct labels. The span of such a labelling is the difference between the maximum and minimum labels used, and the minimum span over all L(2, 1, 1)-labelings of G is called the L(2, 1, 1)-labeling number of G, denoted by λ2,1,1(G). It was shown by King, Ras and Zhou...

From paths to stars.

Alameddine, A.F. (1991)

International Journal of Mathematics and Mathematical Sciences

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Graphic sequences of trees and a problem of Frobenius

Gautam Gupta, Puneet Joshi, Amitabha Tripathi (2007)

Czechoslovak Mathematical Journal

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We give a necessary and sufficient condition for the existence of a tree of order n with a given degree set. We relate this to a well-known linear Diophantine problem of Frobenius.

Small integral trees.

Brouwer, A.E. (2008)

The Electronic Journal of Combinatorics [electronic only]

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On a matching distance between rooted phylogenetic trees

Damian Bogdanowicz, Krzysztof Giaro (2013)

International Journal of Applied Mathematics and Computer Science

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The Robinson-Foulds (RF) distance is the most popular method of evaluating the dissimilarity between phylogenetic trees. In this paper, we define and explore in detail properties of the Matching Cluster (MC) distance, which can be regarded as a refinement of the RF metric for rooted trees. Similarly to RF, MC operates on clusters of compared trees, but the distance evaluation is more complex. Using the graph theoretic approach based on a minimum-weight perfect matching in bipartite graphs,...