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I am looking for a good text book on Matroid theory. Ideally, one that might be better suited to engineers than pure mathematicians...but any book that is well written/organized would do.

I have just started looking into this area and am working through some survey papers (Wison's "An Introduction to Matroid Theory" and Oxley's "What is a Matroid?")

My university library has a copy of Tutte's book, and I will probably check that out. Just wondering what other people might suggest.

Thanks!

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  • $\begingroup$ I've added the [reference-request] and [matroid-theory] tags. $\endgroup$
    – David Roberts ♦
    Commented Jun 14, 2011 at 7:15
  • $\begingroup$ thanks David...I was looking for tags like those and couldn't find them! $\endgroup$
    – dan
    Commented Jun 14, 2011 at 7:45
  • $\begingroup$ If you're interested in rigidity, the book of Graver, Servatius, Servatius "Combinatorial Rigidity" contains a brief introduction to matroids in that context. $\endgroup$
    – j.c.
    Commented Jun 14, 2011 at 19:45
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    $\begingroup$ Since David Speyer's answer below just bumped this up to the front page, I figured I'd take the opportunity to retag as a book-related question. $\endgroup$
    – David White
    Commented Jun 28, 2011 at 17:20

6 Answers 6

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My first recommendation would be Oxley's Matroid Theory. The second edition was just released this year (19 years after the original), so this is a very 'modern' textbook.

Another option would be Welsh's Matroid Theory. This is an older book (it predates even Oxley's first edition), but is nicely written with a more geometric flavour. Also, I just found out that Welsh's book recently became available as a Dover paperback, so it's very cheap if you want to buy it.

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  • $\begingroup$ I picked up Welsh's book, as it really is cheap enough to go for it. I do like his presentation and exposition so far...thanks $\endgroup$
    – dan
    Commented Jun 29, 2011 at 15:31
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My usual recommendations are Theory of Matroids and Matroid Applications. These are multi-author volumes edited by N. White, and he has done a great job choosing authors and homogenizing notation. Although I believe the second volume was intended to be more applied, I didn't really feel there was a difference between the two in this regard.

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    $\begingroup$ I really like these books, though my feeling is that they're more advanced texts and less suitable for the beginner. However, for certain specific topics, these books contain the best expository treatments I know. You may want to look through their tables of contents on Amazon before going to the trouble of tracking them down. $\endgroup$
    – Timothy Chow
    Commented Jun 28, 2011 at 20:54
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I just discovered this nice book that was published this year

It is an undergraduate textbook on matroids! (Maybe the first undergraduate one completely devoted to matroids?) And from what I could see from the first few chapters, it is highly pedagogical and very well written.

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Textbooks on matroids can be a bit heavy. I suggest the following two:

1) Aigner's classical Combinatorial Theory textbook which has two lengthy and well written chapters on matroids, totaling about 140 pp. Some material is a bit dated (historical notes, refs, etc.) but it's great as an introduction, and recent surveys will fill you in on modern developments.

2) Vol. B of Schrijver's Combinatorial Optimization monograph. It's not really a textbook and it covers only certain topics in matroid theory, but it might be better suited for applications you need, and is terrifically written.

Good luck!

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  • $\begingroup$ Thanks Igor! Is Schrijver's book "Matroids and linking systems" any good? I can find that in the library, but the other references don't seem to be around... $\endgroup$
    – dan
    Commented Jun 14, 2011 at 10:02
  • $\begingroup$ Matroids and linking systems is similar to the material in Schrijver's thesis as well as some papers he wrote around the same time with "linking system" in the title. The papers are not a bad substitute, but the book has longer discussion generally of high quality. $\endgroup$
    – Dave Pritchard
    Commented Oct 27, 2011 at 16:30
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I agree that Tony Huynh's suggestions of Oxley and Welsh are good ones. Depending on what you mean by "suited to engineers," another option might be Lawler's Combinatorial Optimization: Networks and Matroids. Lawler's book focuses on the algorithmic aspects of matroids. Lawler's book was reprinted by Dover but it now seems to be out of print again. :-( However, it seems that you can still find inexpensive copies for sale on the web easily enough.

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My first recommendation would be Oxley's Matroid Theory (Oxley J. G., Matroid Theory, Oxford University Press, Oxford, 1992). It is a well organized textbook. If you are looking for application, Recski A., Matroid Theory and its Applications, Springer Verlag, Berlin (1989) would be best option.

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    $\begingroup$ The first book you mention is already in an answer... $\endgroup$
    – András Bátkai
    Commented Dec 11, 2015 at 16:10

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