Open AccessDegree sums and dense spanning trees
Author(s) -
Tao Li,
Yingqi Gao,
Qiankun Dong,
Hua Wang
Publication year - 2017
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0184912
Subject(s) - spanning tree , minimum spanning tree , combinatorics , degree (music) , heuristics , minimum degree spanning tree , vertex (graph theory) , kruskal's algorithm , mathematics , discrete mathematics , computer science , graph , mathematical optimization , physics , acoustics
Finding dense spanning trees (DST) in unweighted graphs is a variation of the well studied minimum spanning tree problem (MST). We utilize established mathematical properties of extremal structures with the minimum sum of distances between vertices to formulate some general conditions on the sum of vertex degrees. We analyze the performance of various combinations of these degree sum conditions in finding dense spanning subtrees and apply our approach to practical examples. After briefly describing our algorithm we also show how it can be used on variations of DST, motivated by variations of MST. Our work provide some insights on the role of various degree sums in forming dense spanning trees and hopefully lay the foundation for finding fast algorithms or heuristics for related problems.