Two-connected orientations of Eulerian graphs

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

Harary index of Eulerian graphs

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

scholarly journals A note on collapsible graphs and super-Eulerian graphs

2012 ◽  
Vol 312 (15) ◽  
pp. 2223-2227 ◽  
Author(s):  
Hao Li ◽  
Weihua Yang
Keyword(s):  
Eulerian Graphs ◽  
Collapsible Graphs

scholarly journals Clustered Planarity: Small Clusters in Eulerian Graphs

2008 ◽  
pp. 303-314 ◽  
Author(s):  
Eva Jelínková ◽  
Jan Kára ◽  
Jan Kratochvíl ◽  
Martin Pergel ◽  
Ondřej Suchý ◽  
...  
Keyword(s):  
Eulerian Graphs ◽  
Clustered Planarity ◽  
Small Clusters

On minimal Eulerian graphs

1981 ◽  
Vol 12 (4) ◽  
pp. 203-205 ◽  
Author(s):  
Christos H. Papadimitriou ◽  
Mihalis Yannakakis
Keyword(s):  
Eulerian Graphs

Graph Theory: A Look Back—The Road Ahead

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Social Networks ◽  
Graph Theory ◽  
The Internet ◽  
The Road ◽  
Eulerian Graphs ◽  
Bridge Problem ◽  
Look Back ◽  
Leonhard Euler ◽  
The Subject ◽  
The 1960S

This book concludes with an epilogue, which traces the evolution of graph theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution led to the subject of Eulerian graphs, to the various efforts to solve the Four Color Problem. It considers elements of graph theory found in games and puzzles of the past, and the famous mathematicians involved including Sir William Rowan Hamilton and William Tutte. It also discusses the remarkable increase since the 1960s in the number of mathematicians worldwide devoted to graph theory, along with research journals, books, and monographs that have graph theory as a subject. Finally, it looks at the growth in applications of graph theory dealing with communication and social networks and the Internet in the digital age and the age of technology.

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