A note on collapsible graphs and super-Eulerian graphs

Hao Li; Weihua Yang

doi:10.1016/j.disc.2012.04.016

A note on collapsible graphs and super-Eulerian graphs

Discrete Mathematics ◽

10.1016/j.disc.2012.04.016 ◽

2012 ◽

Vol 312 (15) ◽

pp. 2223-2227 ◽

Cited By ~ 2

Author(s):

Hao Li ◽

Weihua Yang

Keyword(s):

Eulerian Graphs ◽

Collapsible Graphs

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Harary index of Eulerian graphs

Journal of Mathematical Chemistry ◽

10.1007/s10910-021-01246-2 ◽

2021 ◽

Author(s):

Junqing Cai ◽

Panpan Wang ◽

Linlin Zhang

Keyword(s):

Harary Index ◽

Eulerian Graphs

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Two-connected orientations of Eulerian graphs

Journal of Graph Theory ◽

10.1002/jgt.20158 ◽

2006 ◽

Vol 52 (3) ◽

pp. 230-242 ◽

Cited By ~ 8

Author(s):

Alex R. Berg ◽

Tibor Jordán

Keyword(s):

Eulerian Graphs

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Traversing Graphs

The Fascinating World of Graph Theory ◽

10.23943/princeton/9780691175638.003.0005 ◽

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.

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Subsemi-Eulerian graphs

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171282000520 ◽

1982 ◽

Vol 5 (3) ◽

pp. 553-564 ◽

Cited By ~ 2

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.

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