A Note on the Degree Condition of Completely Independent Spanning Trees

A Note on the Degree Condition of Completely Independent Spanning Trees

Given a graph G, a set of spanning trees of G are completely independent if for any vertices x and y, the paths connecting them on these trees have neither vertex nor edge in common, except x and y. In this paper, we prove that for graphs of order n, with n ≥ 6, if the minimum degree is at least n-2...

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Veröffentlicht in:IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Communications and Computer Sciences, 2015/10/01, Vol.E98.A(10), pp.2191-2193
Hauptverfasser: CHANG, Hung-Yi, WANG, Hung-Lung, YANG, Jinn-Shyong, CHANG, Jou-Ming
Format: Artikel
Sprache:eng
Schlagworte:
completely independent trees
Dirac's condition
Graph theory
Graphs
Joining
Ore's condition
Trees
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Zusammenfassung:Given a graph G, a set of spanning trees of G are completely independent if for any vertices x and y, the paths connecting them on these trees have neither vertex nor edge in common, except x and y. In this paper, we prove that for graphs of order n, with n ≥ 6, if the minimum degree is at least n-2, then there are at least ⌊n/3⌋ completely independent spanning trees.
ISSN:0916-8508
1745-1337
DOI:10.1587/transfun.E98.A.2191