## The path of a blossom 3

### Edmonds’ Blossom Algorithm - Stanford University

1 Introduction Edmonds’ Blossom algorithm is a polynomial time algorithm for ﬁnding a maximum matchinginagraph. Deﬁnition1.1. InagraphG,amatching isasubsetofedgesofG suchthatnovertex

### Finding&aMaximum&Matching& in&Non1Bipar5te&Graphs&

Finding&aMaximum&Matching& in&Non1Bipar5te&Graphs& Alicia Thilani&Singham&Goodwin& 18.304&•3/22/2013& &

http://math.mit.edu/~rothvoss/18.304.1PM/Presentations/2-Alicia-ATSG2.pdf

### General Matching

some augmenting path) ... Blossom {3,4,5,6,7} is grown in . two different alt-paths. Node 5 is an inner node on path P1, and an outer node on path P2. Similarly, each node in …

https://www.comp.nus.edu.sg/~cs6234/2009/Lectures/Match-sl-PC.pdf

### Performance Studies of the Blossom V Algorithm

Key words. matching, perfect matching, augmenting path, blossom, blossom shrinking AMS subject classi cations (2010). 05C70, 68R10 1 Introduction Blossom V is a powerful algorithm which nds a perfect matching of minimum cost in a graph [6]. Jack Edmonds (1965) developed the rst installment of the Blossom algorithm

https://pdfs.semanticscholar.org/2a21/c37f74e03a91668e51a96542dfcfb9638092.pdf

### Maximum matching in bipartite and non-bipartite graphs

The process stop either when an augmenting path or a blossom are found, or when there are no more unlabeled and unmatched edges or unexplored edges touching at least one EVEN vertex. Lemma 3.1 If there is an augmenting path with respect to M, then the above process nds an augmenting path or a blossom. The running time is O(m).

http://www.cs.tau.ac.il/~zwick/grad-algo-0910/match.pdf

### Edmonds’ Blossom Algorithm - Stanford University

1 Introduction Edmonds’ Blossom algorithm is a polynomial time algorithm for ﬁnding a maximum matchinginagraph. Deﬁnition1.1. InagraphG,amatching isasubsetofedgesofG suchthatnovertex

https://stanford.edu/~rezab/classes/cme323/S16/projects_reports/shoemaker_vare.pdf

### Matchings in Graphs

augmenting path in G, augment the matching and start afresh. Otherwise, by Claim 3, the path yields a blossom, and we shrink it (and also shrink the current matching with respect to it) and continue. If no such directed paths are found, report the current matching. To ﬁnd directed paths eﬃciently, the algorithm maintains a forest of scanned ...

https://www.imsc.res.in/~meena/matching/edmonds.pdf

### How to ﬁnd an augmenting path? Flowers and Blossoms

2. A blossom spans 2k‡1 nodes and contains k matched edges for some integer k 1. The matched edges match all nodes of the blossom except the base. 3. The base of a blossom is an even node (if the stem is part of an alternating tree starting at r). 19 Maximum Matching in …

http://wwwalbers.in.tum.de/lehre/2016WS/ea/split/sec-Maximum-Matching-in-General-Graphs-handout.pdf

### How to ﬁnd an augmenting path? Flowers and Blossoms

2. A blossom spans 2k‡1 nodes and contains k matched edges for some integer k 1. The matched edges match all nodes of the blossom except the base. 3. The base of a blossom is an even node (if the stem is part of an alternating tree starting at r). 20 Maximum Matching in General Graphs15. Oct. 2018 Ernst Mayr, Harald Räcke 571/589

http://wwwalbers.in.tum.de/lehre/2018WS/ea/split/sec-Maximum-Matching-in-General-Graphs-handout.pdf

### How to ﬁnd an augmenting path? Flowers and Blossoms

2. A blossom spans 2k‡1 nodes and contains k matched edges for some integer k 1. The matched edges match all nodes of the blossom except the base. 3. The base of a blossom is an even node (if the stem is part of an alternating tree starting at r). 19 Maximum Matching in General Graphs ©Harald Räcke 535

http://wwwmayr.in.tum.de/lehre/2015WS/ea/split/sec-Maximum-Matching-in-General-Graphs-handout.pdf