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Enumeration for spanning trees and forests of join graphs based on the combinatorial decomposition
Electronic Journal of Graph Theory and Applications, 2016 This paper discusses the enumeration for rooted spanning trees and forests of the labelled join graphs $K_m+H_n$ and $K_m+K_{n,p}$, where $H_n$ is a graph with $n$ isolated vertices.
Sung Sik U
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Low-Degree Spanning Trees of Small Weight [PDF]
, 1996 The degree-d spanning tree problem asks for a minimum-weight spanning tree in which the degree of each vertex is at most d. When d=2 the problem is TSP, and in this case, the well-known Christofides algorithm provides a 1.5-approximation algorithm ...
Balaji Raghavachari +3 more
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Chain-Constrained Spanning Trees [PDF]
Mathematical Programming, 2013 We consider the problem of finding a spanning tree satisfying a family of additional constraints. Several settings have been considered previously, the most famous being the problem of finding a spanning tree with degree constraints. Since the problem is hard, the goal is typically to find a spanning tree that violates the constraints as little as ...
Olver, Neil, Zenklusen, Rico
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Lower-Stretch Spanning Trees [PDF]
SIAM Journal on Computing, 2005 We prove that every weighted graph contains a spanning tree subgraph of average stretch O((log n log log n)^2). Moreover, we show how to construct such a tree in time O(m log^2 n).
Elkin, Michael +3 more
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Brief Announcement: Faster Asynchronous MST and Low Diameter Tree Construction with Sublinear Communication [PDF]
, 2019 Building a spanning tree, minimum spanning tree (MST), and BFS tree in a distributed network are fundamental problems which are still not fully understood in terms of time and communication cost.
King, Valerie, Mashreghi, Ali
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Edge-Preserving Stereo Matching Using Minimum Spanning Tree
IEEE Access, 2019 Despite that the accuracy and efficiency of stereo matching technology have significantly improved in the past decades, the issue of edge-blurring remains a challenge to most of the existing approaches.
Congxuan Zhang +5 more
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IET Computer Vision, 2020 Nowadays, a large number of deep convolutional neural network (CNN) models are applied to image classification tasks. However, the authors find that the most widely used evaluation indicator, the Top‐N Accuracy indicator, cannot discriminate these models
Yuntao Liu, Yong Dou, Peng Qiao
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Spanning trees with a bounded number of leaves [PDF]
Opuscula Mathematica, 2017 In 1998, H. Broersma and H. Tuinstra proved that: Given a connected graph \(G\) with \(n\geq 3\) vertices, if \(d(u)+d(v)\geq n-k+1\) for all non-adjacent vertices \(u\) and \(v\) of \(G\) (\(k\geq 1\)), then \(G\) has a spanning tree with at most \(k ...
Junqing Cai +3 more
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Conditions for Implicit-Degree Sum for Spanning Trees with Few Leaves in K1,4-Free Graphs
Mathematics, 2023 A graph with n vertices is called an n-graph. A spanning tree with at most k leaves is referred to as a spanning k-ended tree. Spanning k-ended trees are important in various fields such as network design, graph theory, and communication networks.
Junqing Cai +3 more
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Spanning trees without adjacent vertices of degree 2
, 2019 Albertson, Berman, Hutchinson, and Thomassen showed in 1990 that there exist highly connected graphs in which every spanning tree contains vertices of degree 2.
Lyngsie, Kasper Szabo, Merker, Martin
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