--- 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]: [^2]: [^3]: [^4]: [^5]: [^6]: [^7]: [^8]: [^9]: