Oberwolfach rectangular table negotiation problem

Dalibor Froncek

doi:10.1016/j.disc.2008.02.034

Oberwolfach rectangular table negotiation problem

Dalibor Froncek

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We completely solve certain case of a "two delegation negotiation" version of the Oberwolfach problem, which can be stated as follows. Let H (k, 3) be a bipartite graph with bipartition X = {x₁, x₂, ..., x_k}, Y = {y₁, y₂, ..., y_k} and edges x₁ y₁, x₁ y₂, x_k y_{k - 1}, x_k y_k, and x_i y_{i - 1}, x_i y_i, x_i y_{i + 1} for i = 2, 3, ..., k - 1. We completely characterize all complete bipartite graphs K_{n, n} that can be factorized into factors isomorphic to G = m H (k, 3), where k is odd and m H (k, 3) is the graph consisting of m disjoint copies of H (k, 3).

Original language	English (US)
Pages (from-to)	501-504
Number of pages	4
Journal	Discrete Mathematics
Volume	309
Issue number	2
DOIs	https://doi.org/10.1016/j.disc.2008.02.034
State	Published - Jan 28 2009

Bibliographical note

Funding Information:
Research for this article was supported by the University of Minnesota Duluth Grant 177–1009. The author would like to thank the anonymous referee whose comments helped to improve the paper.

Keywords

Graph decomposition
Oberwolfach problem

Access

10.1016/j.disc.2008.02.034

OpenUrl availability

Full text

Cite this

@article{dee321cb685a404da97a98874a54cd84,

title = "Oberwolfach rectangular table negotiation problem",

abstract = "We completely solve certain case of a {"}two delegation negotiation{"} version of the Oberwolfach problem, which can be stated as follows. Let H (k, 3) be a bipartite graph with bipartition X = {x1, x2, ..., xk}, Y = {y1, y2, ..., yk} and edges x1 y1, x1 y2, xk yk - 1, xk yk, and xi yi - 1, xi yi, xi yi + 1 for i = 2, 3, ..., k - 1. We completely characterize all complete bipartite graphs Kn, n that can be factorized into factors isomorphic to G = m H (k, 3), where k is odd and m H (k, 3) is the graph consisting of m disjoint copies of H (k, 3).",

keywords = "Graph decomposition, Oberwolfach problem",

author = "Dalibor Froncek",

note = "Funding Information: Research for this article was supported by the University of Minnesota Duluth Grant 177–1009. The author would like to thank the anonymous referee whose comments helped to improve the paper. ",

year = "2009",

month = jan,

day = "28",

doi = "10.1016/j.disc.2008.02.034",

language = "English (US)",

volume = "309",

pages = "501--504",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "2",

}

TY - JOUR

T1 - Oberwolfach rectangular table negotiation problem

AU - Froncek, Dalibor

N1 - Funding Information: Research for this article was supported by the University of Minnesota Duluth Grant 177–1009. The author would like to thank the anonymous referee whose comments helped to improve the paper.

PY - 2009/1/28

Y1 - 2009/1/28

N2 - We completely solve certain case of a "two delegation negotiation" version of the Oberwolfach problem, which can be stated as follows. Let H (k, 3) be a bipartite graph with bipartition X = {x1, x2, ..., xk}, Y = {y1, y2, ..., yk} and edges x1 y1, x1 y2, xk yk - 1, xk yk, and xi yi - 1, xi yi, xi yi + 1 for i = 2, 3, ..., k - 1. We completely characterize all complete bipartite graphs Kn, n that can be factorized into factors isomorphic to G = m H (k, 3), where k is odd and m H (k, 3) is the graph consisting of m disjoint copies of H (k, 3).

AB - We completely solve certain case of a "two delegation negotiation" version of the Oberwolfach problem, which can be stated as follows. Let H (k, 3) be a bipartite graph with bipartition X = {x1, x2, ..., xk}, Y = {y1, y2, ..., yk} and edges x1 y1, x1 y2, xk yk - 1, xk yk, and xi yi - 1, xi yi, xi yi + 1 for i = 2, 3, ..., k - 1. We completely characterize all complete bipartite graphs Kn, n that can be factorized into factors isomorphic to G = m H (k, 3), where k is odd and m H (k, 3) is the graph consisting of m disjoint copies of H (k, 3).

KW - Graph decomposition

KW - Oberwolfach problem

UR - http://www.scopus.com/inward/record.url?scp=56649111427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56649111427&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2008.02.034

DO - 10.1016/j.disc.2008.02.034

M3 - Article

AN - SCOPUS:56649111427

SN - 0012-365X

VL - 309

SP - 501

EP - 504

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -

Oberwolfach rectangular table negotiation problem

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this