<p>Are there necessary and sufficient conditions for a uniform hyper graph to have a perfect fractional matching ? </p>

CC BY-SA 3.0
2012-06-14T13:34:42.323Z
The definition is already a nice characterization. What are you looking for? A necessary and sufficient condition that is combinatorial?
Tsuyoshi Ito
CC BY-SA 3.0
2012-06-14T16:20:41.197Z
Could you provide some context, background, and motivation?
Kaveh
CC BY-SA 3.0
2012-06-15T07:52:54.550Z
To me it seem that if you can solve the problem quickly in uniform hypergraphs, you can also solve the problem quickly in arbitrary hypergraphs – just add gadgets that make the hypergraph uniform while preserving the existence of a perfect fractional matching. And in the case of arbitrary hypergraphs, it seems to me that the problem is almost as difficult as solving a general 0/1 packing LP. Hence I would not expect that there is a particularly useful formulation of a necessary & sufficient condition.
Jukka Suomela
<co.combinatorics><matching>
Perfect fractional matching of uniform hyper graph
Mikhail
# Perfect fractional matching of uniform hyper graph

(Asked by: username_0 on 2012-06-14)

Are there necessary and sufficient conditions for a uniform hyper graph to have a perfect fractional matching ?

**Tags:** co.combinatorics, matching
> **Comments:**
> **username_1**: The definition is already a nice characterization. What are you looking for? A necessary and sufficient condition that is combinatorial?  
> **username_2**: Could you provide some context, background, and motivation?  
> **username_3**: To me it seem that if you can solve the problem quickly in uniform hypergraphs, you can also solve the problem quickly in arbitrary hypergraphs – just add gadgets that make the hypergraph uniform while preserving the existence of a perfect fractional matching. And in the case of arbitrary hypergraphs, it seems to me that the problem is almost as difficult as solving a general 0/1 packing LP. Hence I would not expect that there is a particularly useful formulation of a necessary & sufficient condition.  

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## 0 answers

