Directed Rooted Forests in Higher Dimension
نویسندگان
چکیده
منابع مشابه
Directed Rooted Forests in Higher Dimension
For a graph G, the generating function of rooted forests, counted by the number of connected components, can be expressed in terms of the eigenvalues of the graph Laplacian. We generalize this result from graphs to cell complexes of arbitrary dimension. This requires generalizing the notion of rooted forest to higher dimension. We also introduce orientations of higher dimensional rooted trees a...
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If F,G are two n×m matrices, then det(1+xFG) = ∑ P x |P det(FP )det(GP ) where the sum is over all minors [19]. An application is a new proof of the Chebotarev-Shamis forest theorem telling that det(1 + L) is the number of rooted spanning forests in a finite simple graph G with Laplacian L. We can generalize this and show that det(1 + kL) is the number of rooted edge-k-colored spanning forests....
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Erdos, P. L., A new bijection on rooted forests, Discrete Mathematics 111 (1993) 179-188. This paper extends the method due to Szekely and ErdBs (1989) on the enumeration of trees. A bijection is introduced on certain classes of rooted forests (more exactly, on the class of semilabelled forests). This method yields new easy proofs for some well-known theorems which use only elementary calculati...
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An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighborhood of the third vertex. Asteroidal triples play a central role in a classical characterization of interval graphs by Lekkerkerker and Boland. Their result says that a chordal graph is an interval graph if and only if it contains no asteroidal triple. In this paper, we prove a...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5819