Edge coloring a K-tree into two smaller trees

26 Pages·1993·1.7 MB·English

by  Chhajed, Dilip

UNIVERSITY OF
ILLINOIS LiHRARY
AT URBANA-Ci 1A1VIPAIGN
BOOKSTACKS
Digitized by the Internet Archive
in 2012 with funding from
University of Illinois Urbana-Champaign
http://www.archive.org/details/edgecoloringktre165chha

Faculty Working Paper 93-0165
330 ;~rx
B385
i??3:165 COPY 2
Edge Coloring A K-Tree Into Two Smaller Trees
THf
U
^ ****y
Of
rHe
'J.
V/».,
Dilip Chhajed
DepartmentofBusinessAdministration
University ofIllinois
BureauofEconomicand Business Research
CollegeofCommerceand BusinessAdministration
University ofIllinois at Urbana-Champaign

BEBR
FACULTY WORKING PAPER NO. 93-0165
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
October 1993
Edge Coloring A K-Tree Into Two Smaller Trees
Dilip Chhajed
Department of Business Administration

Edge Coloring A K-Tree Into Two Smaller Trees
Dilip Chhajed
Department ofBusiness Administration
University ofIllinois
350 Commerce West
Champaign, IL 61820
email: [email protected]
September 1993
Abstract
The problem ofedge coloring partial k-tree into two partial p- and q-trees with p,q<k is
considered. An algorithm is provided to construct such a coloring with p+q=k. Usefulness
ofthis result in a Lagrangian decomposition framework to solve certain combinatorial
optimization problems is discussed.
Keywords: Networks/Graphs: Theory; Facilities Planning: Location;Analysis of
Algorithms: Suboptimal Algorithms
Acknowledgments: I would like to thank Refael Hassin and Charles Blair for their
comments on an earlierdraft ofthis paper.