scholarly journals Maximum cycle packing in Eulerian graphs using local traces

2015 ◽  
Vol 35 (1) ◽  
pp. 121 ◽  
Author(s):  
Peter Recht ◽  
Eva-Maria Sprengel
Keyword(s):  
Eulerian Graphs ◽  
Cycle Packing

Harary index of Eulerian graphs

2021 ◽  
Author(s):  
Junqing Cai ◽  
Panpan Wang ◽  
Linlin Zhang
Keyword(s):  
Harary Index ◽  
Eulerian Graphs

Two-connected orientations of Eulerian graphs

2006 ◽  
Vol 52 (3) ◽  
pp. 230-242 ◽  
Author(s):  
Alex R. Berg ◽  
Tibor Jordán
Keyword(s):  
Eulerian Graphs

Traversing Graphs

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Chinese Postman Problem ◽  
Round Trip ◽  
Eulerian Graphs ◽  
Bridge Problem ◽  
Chinese Postman ◽  
Leonhard Euler ◽  
The City ◽  
East Prussia

This chapter considers Eulerian graphs, a class of graphs named for the Swiss mathematician Leonhard Euler. It begins with a discussion of the the Königsberg Bridge Problem and its connection to Euler, who presented the first solution of the problem in a 1735 paper. Euler showed that it was impossible to stroll through the city of Königsberg, the capital of German East Prussia, and cross each bridge exactly once. He also mentioned in his paper a problem whose solution uses the geometry of position to which Gottfried Leibniz had referred. The chapter concludes with another problem, the Chinese Postman Problem, which deals with minimizing the length of a round-trip that a letter carrier might take.

scholarly journals Subsemi-Eulerian graphs

1982 ◽  
Vol 5 (3) ◽  
pp. 553-564 ◽  
Author(s):  
Charles Suffel ◽  
Ralph Tindell ◽  
Cynthia Hoffman ◽  
Manachem Mandell
Keyword(s):  
Eulerian Graphs ◽  
Related Notion ◽  
Minimum Number ◽  
Eulerian Graph

A graph is subeulerian if it is spanned by an eulerian supergraph. Boesch, Suffel and Tindell have characterized the class of subeulerian graphs and determined the minimum number of additional lines required to make a subeulerian graph eulerian.In this paper, we consider the related notion of a subsemi-eulerian graph, i.e. a graph which is spanned by a supergraph having an open trail containing all of its lines. The subsemi-eulerian graphs are characterized and formulas for the minimum number of required additional lines are given. Interrelationships between the two problems are stressed as well.

scholarly journals MAXIMUM WEIGHT CYCLE PACKING IN DIRECTED GRAPHS, WITH APPLICATION TO KIDNEY EXCHANGE PROGRAMS

2009 ◽  
Vol 01 (04) ◽  
pp. 499-517 ◽  
Author(s):  
PÉTER BIRÓ ◽  
DAVID F. MANLOVE ◽  
ROMEO RIZZI
Keyword(s):  
Directed Graphs ◽  
Exact Algorithm ◽  
Maximum Size ◽  
Practical Experience ◽  
Optimal Solutions ◽  
Maximum Weight ◽  
Packing Problems ◽  
Exchange Programs ◽  
Kidney Exchange ◽  
Cycle Packing

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration.

scholarly journals Cycle packing

2014 ◽  
Vol 45 (4) ◽  
pp. 608-626 ◽  
Author(s):  
David Conlon ◽  
Jacob Fox ◽  
Benny Sudakov
Keyword(s):  
Cycle Packing

scholarly journals Algorithms and outerplanar conditions for A-trails in plane Eulerian graphs

1998 ◽  
Vol 85 (2) ◽  
pp. 99-112 ◽  
Author(s):  
Lars Døvling Andersen ◽  
Herbert Fleischner ◽  
Susanne Regner
Keyword(s):  
Eulerian Graphs
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