IEICE TRANSACTIONS on Fundamentals
Complete Cycle Embedding in Crossed Cubes with Two-Disjoint-Cycle-Cover Pancyclicity
Summary :
A graph G is two-disjoint-cycle-cover r-pancyclic if for any integer l satisfying r≤l≤|V(G)|-r, there exist two vertex-disjoint cycles C1 and C2 in G such that the lengths of C1 and C2 are |V(G)|-l and l, respectively, where |V(G)| denotes the total number of vertices in G. In particular, the graph G is two-disjoint-cycle-cover vertex r-pancyclic if for any two distinct vertices u and v of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains u, (ii) C2 contains v, and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. Moreover, G is two-disjoint-cycle-cover edge r-pancyclic if for any two vertex-disjoint edges (u,v) and (x,y) of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains (u,v), (ii) C2 contains (x,y), and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. In this paper, we first give Dirac-type sufficient conditions for general graphs to be two-disjoint-cycle-cover vertex/edge 3-pancyclic, and we also prove that the n-dimensional crossed cube CQn is two-disjoint-cycle-cover 4-pancyclic for n≥3, vertex 4-pancyclic for n≥5, and edge 6-pancyclic for n≥5.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.12 pp.2670-2676
- Publication Date
- 2015/12/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E98.A.2670
- Type of Manuscript
- PAPER
- Category
- Graphs and Networks
Authors
Tzu-Liang KUNG
Asia University
Hon-Chan CHEN
National Chin-Yi University of Technology
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Tzu-Liang KUNG, Hon-Chan CHEN, "Complete Cycle Embedding in Crossed Cubes with Two-Disjoint-Cycle-Cover Pancyclicity" in IEICE TRANSACTIONS on Fundamentals,
vol. E98-A, no. 12, pp. 2670-2676, December 2015, doi: 10.1587/transfun.E98.A.2670.
Abstract: A graph G is two-disjoint-cycle-cover r-pancyclic if for any integer l satisfying r≤l≤|V(G)|-r, there exist two vertex-disjoint cycles C1 and C2 in G such that the lengths of C1 and C2 are |V(G)|-l and l, respectively, where |V(G)| denotes the total number of vertices in G. In particular, the graph G is two-disjoint-cycle-cover vertex r-pancyclic if for any two distinct vertices u and v of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains u, (ii) C2 contains v, and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. Moreover, G is two-disjoint-cycle-cover edge r-pancyclic if for any two vertex-disjoint edges (u,v) and (x,y) of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains (u,v), (ii) C2 contains (x,y), and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. In this paper, we first give Dirac-type sufficient conditions for general graphs to be two-disjoint-cycle-cover vertex/edge 3-pancyclic, and we also prove that the n-dimensional crossed cube CQn is two-disjoint-cycle-cover 4-pancyclic for n≥3, vertex 4-pancyclic for n≥5, and edge 6-pancyclic for n≥5.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.2670/_p
Copy
@ARTICLE{e98-a_12_2670,
author={Tzu-Liang KUNG, Hon-Chan CHEN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Complete Cycle Embedding in Crossed Cubes with Two-Disjoint-Cycle-Cover Pancyclicity},
year={2015},
volume={E98-A},
number={12},
pages={2670-2676},
abstract={A graph G is two-disjoint-cycle-cover r-pancyclic if for any integer l satisfying r≤l≤|V(G)|-r, there exist two vertex-disjoint cycles C1 and C2 in G such that the lengths of C1 and C2 are |V(G)|-l and l, respectively, where |V(G)| denotes the total number of vertices in G. In particular, the graph G is two-disjoint-cycle-cover vertex r-pancyclic if for any two distinct vertices u and v of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains u, (ii) C2 contains v, and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. Moreover, G is two-disjoint-cycle-cover edge r-pancyclic if for any two vertex-disjoint edges (u,v) and (x,y) of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains (u,v), (ii) C2 contains (x,y), and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. In this paper, we first give Dirac-type sufficient conditions for general graphs to be two-disjoint-cycle-cover vertex/edge 3-pancyclic, and we also prove that the n-dimensional crossed cube CQn is two-disjoint-cycle-cover 4-pancyclic for n≥3, vertex 4-pancyclic for n≥5, and edge 6-pancyclic for n≥5.},
keywords={},
doi={10.1587/transfun.E98.A.2670},
ISSN={1745-1337},
month={December},}
Copy
TY - JOUR
TI - Complete Cycle Embedding in Crossed Cubes with Two-Disjoint-Cycle-Cover Pancyclicity
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2670
EP - 2676
AU - Tzu-Liang KUNG
AU - Hon-Chan CHEN
PY - 2015
DO - 10.1587/transfun.E98.A.2670
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2015
AB - A graph G is two-disjoint-cycle-cover r-pancyclic if for any integer l satisfying r≤l≤|V(G)|-r, there exist two vertex-disjoint cycles C1 and C2 in G such that the lengths of C1 and C2 are |V(G)|-l and l, respectively, where |V(G)| denotes the total number of vertices in G. In particular, the graph G is two-disjoint-cycle-cover vertex r-pancyclic if for any two distinct vertices u and v of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains u, (ii) C2 contains v, and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. Moreover, G is two-disjoint-cycle-cover edge r-pancyclic if for any two vertex-disjoint edges (u,v) and (x,y) of G, there exist two vertex-disjoint cycles C1 and C2 in G such that (i) C1 contains (u,v), (ii) C2 contains (x,y), and (iii) the lengths of C1 and C2 are |V(G)|-l and l, respectively, for any integer l satisfying r≤l≤|V(G)|-r. In this paper, we first give Dirac-type sufficient conditions for general graphs to be two-disjoint-cycle-cover vertex/edge 3-pancyclic, and we also prove that the n-dimensional crossed cube CQn is two-disjoint-cycle-cover 4-pancyclic for n≥3, vertex 4-pancyclic for n≥5, and edge 6-pancyclic for n≥5.
ER -
English
