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   Vol.E100-A   No.9   pp.1932-1935
Publication Date: 2017/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.1932
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.