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Completely Independent Spanning Trees on 4-Regular Chordal Rings
Jou-Ming CHANG Hung-Yi CHANG Hung-Lung WANG Kung-Jui PAI Jinn-Shyong YANG
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2017/09/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section LETTER (Special Section on Discrete Mathematics and Its Applications)
completely independent spanning trees, chordal rings, distributed loop networks,
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Given a graph G, a set of spanning trees of G are completely independent spanning trees (CISTs for short) 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. Hasunuma (2001, 2002) first introduced the concept of CISTs and conjectured that there are k CISTs in any 2k-connected graph. Later on, this conjecture was unfortunately disproved by Péterfalvi (2012). In this note, we show that Hasunuma's conjecture holds for graphs restricted in the class of 4-regular chordal rings CR(n,d), where both n and d are even integers.