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Exponentially many perfect matchings in cubic graphs
Exponentially many perfect matchings cubic graphs
2011/1/21
We show that every cubic bridgeless graph G has at least 2|V (G)|/3656 perfect matchings.
This confirms an old conjecture of Lov´asz and Plummer.
Partitions and Partial Matchings Avoiding Neighbor Patterns
set partition partial matching neighbor alignment left nesting right nesting
2010/12/10
We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there is a bijection betwee...
A Major Index for Matchings and Set Partitions
tangled-diagram partition matching crossing nesting vacillating tableau
2014/6/3
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...
A Major Index for Matchings and Set Partitions
tangled-diagram partition matching crossing nesting vacillating tableau
2014/6/3
A tangled diagram on [n] = {1,..., n} is a labeled graph for which each vertex has degree at most two. The vertices are arranged in increasing order on a horizontal line and the arcs are drawn in the ...