---
categories: Combinatorial optimization
---

## Matroid partitioning
Matroid partitioning can be reduced to Matroid intersection [^8].

## Problems
- [Royal Questions](http://codeforces.com/contest/875/problem/F) [^6] [^7]
- [Red/Blue Spanning Tree](https://open.kattis.com/problems/redbluetree)
- [Rainbow Graph](https://open.kattis.com/problems/rainbowgraph) [^1]
- [FoxAirline2](https://community.topcoder.com/stat?c=problem_statement&pm=14194&rd=16689)
- [ColoringEdgesDiv1](https://community.topcoder.com/stat?c=problem_statement&pm=14909&rd=17198) [^2]
- [JobPlanner](https://community.topcoder.com/stat?c=problem_statement&pm=6177) [^3]
- [Seollal](http://codeforces.com/contest/1284/problem/G) [^9]
- [XorGame](https://contest.yandex.com/algorithm2017/contest/4737/problems/F/) [^4] [^5]

## See also
- [Minimum spanning tree]()
- [Bipartite matching]()
- [Minimum Cost Arborescence]()
- [Maximum flow]()

## External links
- [Matroid](https://en.wikipedia.org/wiki/Matroid)
- [Matroid intersection](https://en.wikipedia.org/wiki/Matroid_intersection)
- [Matroid partitioning](https://en.wikipedia.org/wiki/Matroid_partitioning)
- [Dual matroid](https://en.wikipedia.org/wiki/Dual_matroid)
- [Graphic matroid](https://en.wikipedia.org/wiki/Graphic_matroid)
- [Arboricity](https://en.wikipedia.org/wiki/Arboricity)
- [Shannon switching game](https://en.wikipedia.org/wiki/Shannon_switching_game)
- [Graph Algorithms and Combinatorial Optimization: Matroid intersection](https://web.archive.org/web/20170829154005/http://www.utdallas.edu/~kam093020/papers/matroid-intersection.pdf)
- [Lecture notes on matroid intersection](http://math.mit.edu/~goemans/18433S11/matroid-intersect-notes.pdf)
- [Combinatorial Optimization: Matroid Intersection](https://courses.engr.illinois.edu/cs598csc/sp2010/Lectures/Lecture17.pdf)
- [Combinatorial Optimization: Weighted Matroid Intersection](https://courses.engr.illinois.edu/cs598csc/sp2010/Lectures/Lecture18.pdf)

[^1]: <http://codeforces.com/blog/entry/58442?#comment-421990>
[^2]: <https://www.topcoder.com/blog/tco18-algorithm-round-3a-editorials/>
[^3]: <https://community.topcoder.com/tc?module=Static&d1=match_editorials&d2=tccc07_rd2>
[^4]: <http://codeforces.com/blog/entry/53354?#comment-374026>
[^5]: <https://www.topcoder.com/blog/how-to-come-up-with-problem-ideas/>
[^6]: <https://petr-mitrichev.blogspot.com/2017/12/a-transversal-week.html>
[^7]: <http://codeforces.com/blog/entry/55201?#comment-390963>
[^8]: <https://codeforces.com/blog/entry/43871?#comment-285163>
[^9]: <http://codeforces.com/blog/entry/72804>