Jump to ContentJump to Main Navigation

You are looking at 1-6 of 6 items for:

  • Keywords: matroid x
  • Mathematics x
Clear All Modify Search

View:

ORBIT COUNTING AND THE TUTTE POLYNOMIAL

Peter J. Cameron

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/9780198571278.003.0001
Subject:
Mathematics, Probability / Statistics

This chapter summarizes the various attempts to extend the Tutte polynomial of a matroid to a polynomial which counts orbits of a group on various sets of objects that the usual Tutte polynomial ... More


THE CONTRIBUTIONS OF DOMINIC WELSH TO MATROID THEORY

James Oxley

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/9780198571278.003.0015
Subject:
Mathematics, Probability / Statistics

Dominic Welsh began writing papers in matroid theory nearly forty years ago. Since then, he has made numerous important contributions to the subject. This chapter reviews Dominic Welsh's work in and ... More


Graphic Matroids

James Oxley

in Matroid Theory

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.003.0006
Subject:
Mathematics, Educational Mathematics

This chapter examines graphic matroids in more detail. In particular, it presents several proofs delayed from Chapters 1 and 2, including proofs that a graphic matroid is representable over every ... More


Representable Matroids

James Oxley

in Matroid Theory

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.003.0007
Subject:
Mathematics, Educational Mathematics

This chapter provides an overview of the basic questions associated with matroid representability and indicates how one actually goes about constructing representations. The key ideas are presented ... More


Excluded-Minor Theorems

James Oxley

in Matroid Theory

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.003.0011
Subject:
Mathematics, Educational Mathematics

This chapter is organized as follows. Section 10.1 presents Gerards' (1989) proof of Tutte's (1958) excluded-minor characterization of the class of regular matroids. Section 10.2 proves the ... More


Submodular Functions and Matroid Union

James Oxley

in Matroid Theory

Published in print:
2011
Published Online:
December 2013
ISBN:
9780198566946
eISBN:
9780191774904
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566946.003.0012
Subject:
Mathematics, Educational Mathematics

This chapter considers several more matroid constructions. The chapter is organized as follows. Section 11.2 considers several applications of submodular functions, one of which is in the proof of ... More


View: