The Matrix-Tree Theorem is a well-known combinatorial result relating the value of the minors of a certain square matrix to the sum of the weights of the arborescences (= rooted directed trees) in the associated graph. We prove an extension of this result to algebraic structures much more general th
Semirings and Tree-to-Graph-to-Tree Transductions
β Scribed by Frank Drewes
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 515 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1571-0661
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The 'All Minors Matrix Tree Theorem' (Chen, Applied Graph Theory, Graphs and Electrical Networks, North-Holland, Amsterdam, 1976; Chaiken, SIAM J. Algebraic Discrete Math. 3 (3) (1982) 319-329) is an extension of the well-known 'Matrix Tree Theorem' (Tutte, Proc. Cambridge Philos. Sot. 44 (1948) 463
The aim of this addendum is to explain more precisely the second part of the proof of Theorem 1 from our paper [1]. We need to show that a.e. graph G e~J(n,p) contains a maximal induced tree of order less than (l+e)X (log n)/(log d). The second moment method used in our Lemma shows in fact that
The following assertions are shown to be equivalent, for any countable graph G: (1) G can be represented as the intersection graph of a family of subtrees of a tree; (2) G admits a tree-decomposition (Robertson/Seymour) into primes; (3) G is chordal, and G admits a simpkial tree-decomposition (Halin