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EULERIAN AND BIPARTITE ORIENTABLE MATROIDS

Laura E. Chávez Lomelí and Luis A. Goddyn

in Combinatorics, Complexity, and Chance: A Tribute to Dominic Welsh

Published in print:
2007
Published Online:
September 2007
ISBN:
9780198571278
eISBN:
9780191718885
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198571278.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter focuses on extending the characterizations of Eulerian graphs via orientations. An Eulerian tour of a graph G induces an orientation with the property that every cocircuit (minimal edge ... More


Analyzing Distance

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0003
Subject:
Mathematics, Applied Mathematics

This chapter considers distance in graphs, first by providing an overview of some fundamental concepts in graph theory. In particular, it discusses connected graphs, cut-vertex and bridge, and ... More


Factoring Graphs

Arthur Benjamin, Gary Chartrand, and Ping Zhang

in The Fascinating World of Graph Theory

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter focuses on Hall's Theorem, introduced by British mathematician Philip Hall, and its connection to graph theory. It first considers problems that ask whether some collection of objects ... More


Graphs and the Dynamics of Biochemical Networks

David Angeli and Eduardo D. Sontag

in Control Theory and Systems Biology

Published in print:
2009
Published Online:
August 2013
ISBN:
9780262013345
eISBN:
9780262258906
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262013345.003.0007
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter describes two approaches, one based on bipartite graphs and Petri net concepts, and another based on decompositions into order-preserving subsystems. It addresses the basic formalism ... More


Bio-inspired Artificial Chemistries

Wolfgang Banzhaf and Lidia Yamamoto

in Artificial Chemistries

Published in print:
2015
Published Online:
September 2016
ISBN:
9780262029438
eISBN:
9780262329460
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262029438.003.0011
Subject:
Public Health and Epidemiology, Public Health

Biological systems have inspired a large number of ACs, naturally of a more complex type. Just as their natural counterparts, such artificial systems show a multitude of phenomena and often cannot ... More


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