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Do you know any references on the use of matching polynomials in computer science, particularly regarding their applications or algorithmic developments?

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  • $\begingroup$ Hello, welcome to CS.SE! Regarding applications or algorithmic developments that is a little vague. Are you just looking for any applications of matching polynomials in computer science? $\endgroup$ Commented Sep 3 at 19:02
  • $\begingroup$ @CalebStanford yes, some applications of that in Computer Science. I'm preparing a proposal and I like to mention something in this field $\endgroup$ Commented Sep 3 at 19:32

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I will not answer the question as asked, but I will offer some advice :)

You mention that you are preparing a proposal in your comment. (You don't say whether the proposal is for a research scholarship or award, or for a research funding organization.) Either way, for the purposes of a proposal, I would suspect it is less important that matching polynomials have specifically been used in computer science. Of course, if you can find a specific application in a paper somewhere, then great! But it may or may not exist, and the applications may or may not have been discovered yet.

Rather, you should aim to motivate why matching polynomials might be of interest to certain applications. For this point, I highly doubt that it is necessary that matching polynomials have been applied specifically. For the idea of matchings themselves has abundant applications in computer science, and indeed, the fact that matchings have important applications is likely far more important (both to the impact of your work, and to its interest to funding bodies, award organizations, or proposal reviewers) compared to some specialized application of matching polynomials. That is, you should aim to motivate your work in the following way:

  • Matchings are of fundamental interest and have many applications, for example matching algorithms are used in computer science for (list a myriad of such applications).

  • Matching polynomials are used to understand matchings and to count how many matchings exist in a graph. This is relevant for (applications above) because it helps us understand (certain aspects that may be relevant, such as how common matchings are, etc.)

  • This work will shed light on matching polynomials by answering (questions XYZ) which tie back to the applications above and could help illuminate matchings due to (reasons ABC).

If you follow such a recipe, I suspect it will have a greater chance of your proposal getting awarded or funded. It is often helpful when thinking about proposals and funding to "zoom out" a level in this way - and to justify your work through another layer of indirection, rather than simply discussing the immediate or known applications so far (which can be quite limiting to your work and its potential applicability).

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    $\begingroup$ These are great suggestions! Thank you very much, I'll really follow them $\endgroup$ Commented Sep 3 at 20:06
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    $\begingroup$ You are welcome! I am glad to hear it will be helpful. $\endgroup$ Commented Sep 3 at 20:37
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I have a paper (that is not yet published) on matching polynomials. Read Chris Godsil's papers on them as a start.

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    $\begingroup$ What paper do you suggest in particular? Is the book "Geometric Algorithms and Combinatorial Optimization" by M. Grötschel, L. Lovász, and A. Schrijver pertinent??? $\endgroup$ Commented Sep 4 at 15:38

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