IEICE TRANSACTIONS on Fundamentals
Independent Spanning Trees of 2-Chordal Rings
Summary :
Two spanning trees T1,T2 of a graph G = (V,E) are independent if they are rooted at the same vertex, say r, and for each vertex v ∈ V, the path from r to v in T1 and the path from r to v in T2 have no common vertices and no common edges except for r and v. In general, spanning trees T1,T2,…,Tk of a graph G = (V,E) are independent if they are pairwise independent. A graph G = (V,E) is called a 2-chordal ring and denoted by CR(N,d1,d2), if V = {0,1,…,N-1} and E = {(u,v)|[v-u]N = 1 or [v-u]N = d1 or [v-u]N = d2, 2 ≤ d1 < d2 ≤ N/2}. CR(N,d1,N/2) is 5-connected if N ≥ 8 is even and d1 ≠ N/2-1. We give an algorithm to construct 5 independent spanning trees of CR(N,d1,N/2),N ≥ 8 is even and 2 ≤ d1 ≤ ⌈N/4⌉.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.1 pp.355-362
- Publication Date
- 2016/01/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E99.A.355
- Type of Manuscript
- PAPER
- Category
- Graphs and Networks
Authors
Yukihiro HAMADA
National Institute of Technology, Akashi College
Keyword
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Yukihiro HAMADA, "Independent Spanning Trees of 2-Chordal Rings" in IEICE TRANSACTIONS on Fundamentals,
vol. E99-A, no. 1, pp. 355-362, January 2016, doi: 10.1587/transfun.E99.A.355.
Abstract: Two spanning trees T1,T2 of a graph G = (V,E) are independent if they are rooted at the same vertex, say r, and for each vertex v ∈ V, the path from r to v in T1 and the path from r to v in T2 have no common vertices and no common edges except for r and v. In general, spanning trees T1,T2,…,Tk of a graph G = (V,E) are independent if they are pairwise independent. A graph G = (V,E) is called a 2-chordal ring and denoted by CR(N,d1,d2), if V = {0,1,…,N-1} and E = {(u,v)|[v-u]N = 1 or [v-u]N = d1 or [v-u]N = d2, 2 ≤ d1 < d2 ≤ N/2}. CR(N,d1,N/2) is 5-connected if N ≥ 8 is even and d1 ≠ N/2-1. We give an algorithm to construct 5 independent spanning trees of CR(N,d1,N/2),N ≥ 8 is even and 2 ≤ d1 ≤ ⌈N/4⌉.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.355/_p
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@ARTICLE{e99-a_1_355,
author={Yukihiro HAMADA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Independent Spanning Trees of 2-Chordal Rings},
year={2016},
volume={E99-A},
number={1},
pages={355-362},
abstract={Two spanning trees T1,T2 of a graph G = (V,E) are independent if they are rooted at the same vertex, say r, and for each vertex v ∈ V, the path from r to v in T1 and the path from r to v in T2 have no common vertices and no common edges except for r and v. In general, spanning trees T1,T2,…,Tk of a graph G = (V,E) are independent if they are pairwise independent. A graph G = (V,E) is called a 2-chordal ring and denoted by CR(N,d1,d2), if V = {0,1,…,N-1} and E = {(u,v)|[v-u]N = 1 or [v-u]N = d1 or [v-u]N = d2, 2 ≤ d1 < d2 ≤ N/2}. CR(N,d1,N/2) is 5-connected if N ≥ 8 is even and d1 ≠ N/2-1. We give an algorithm to construct 5 independent spanning trees of CR(N,d1,N/2),N ≥ 8 is even and 2 ≤ d1 ≤ ⌈N/4⌉.},
keywords={},
doi={10.1587/transfun.E99.A.355},
ISSN={1745-1337},
month={January},}
Copy
TY - JOUR
TI - Independent Spanning Trees of 2-Chordal Rings
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 355
EP - 362
AU - Yukihiro HAMADA
PY - 2016
DO - 10.1587/transfun.E99.A.355
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2016
AB - Two spanning trees T1,T2 of a graph G = (V,E) are independent if they are rooted at the same vertex, say r, and for each vertex v ∈ V, the path from r to v in T1 and the path from r to v in T2 have no common vertices and no common edges except for r and v. In general, spanning trees T1,T2,…,Tk of a graph G = (V,E) are independent if they are pairwise independent. A graph G = (V,E) is called a 2-chordal ring and denoted by CR(N,d1,d2), if V = {0,1,…,N-1} and E = {(u,v)|[v-u]N = 1 or [v-u]N = d1 or [v-u]N = d2, 2 ≤ d1 < d2 ≤ N/2}. CR(N,d1,N/2) is 5-connected if N ≥ 8 is even and d1 ≠ N/2-1. We give an algorithm to construct 5 independent spanning trees of CR(N,d1,N/2),N ≥ 8 is even and 2 ≤ d1 ≤ ⌈N/4⌉.
ER -
English
