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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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