Báo cáo toán học: "Spanning Trees of Bounded Degree" ppsx

... degree of x i is 2, and the degree of a 0 is ∆ − 1. However, the degree of a 1 isthesameinbothtrees,soS wins either by Rule 2 or by Rule 3.  Since P is a maximum path in G, no point of V −P ... ,x k−2 }.Then deg G (u 1 )+deg G (u t )+ k−2  i=1 deg G (x i ) ≥ n − 1. (1) THE ELECTRONIC JOURNAL OF COMB INATORICS 8 (2001), #R33 7 Spanning Trees of Bounded Degree Andrzej Czygrino...

Ngày tải lên: 07/08/2014, 06:22

... E˘gecio˘glu and Remmel [4] who gave a bijective proofoftheformulan n−2 for the number of Cayley trees on n vertices, i.e. the number of spanning trees of the complete graph K n . In particular, they ... (m i ,x  i )isanedgeofG. Thus, any nonloop edge added to Θ −1 j (T ) must be an edge of G so that condition (1) of F n (G, F,q)isalso satisfied. This completes the proof of the...

Ngày tải lên: 07/08/2014, 06:23

Ngày tải lên: 05/08/2014, 10:20

... triangulation of M with f 0 vertices and f 1 edges. Proof: The lemma is a reformulation of Walkup’s Lemmas 7.3 from [46]. The con- dition of the existence of an Hamiltonian cycle in the link of some ... facet of a triangulated d-manifold K is a subset σ of the vertex set of cardinality d + 1 such that σ /∈ K, but every proper subset of σ is a face of K. Definition 15 Let K...

Ngày tải lên: 08/08/2014, 01:20

... boundary walk of ∆ i n meets n +1edges of T n . But any path in the 1-skeleton of ∆ n meeting four distinct edges of T n has combinatorial length at least n. So the length of the boundary walk of ∆ i n is at ... available. The boundary walks of the diagrams ∆ i are then each comprised of a path in T , trails in the 1-skeleta of two T ∗ -galleries of ∆ i , and a portion of...

Ngày tải lên: 07/08/2014, 13:21

Ngày tải lên: 05/08/2014, 15:21

... parameters of σ. The parameters of the empty permutation (of length 0) are (1, 1). Note that for any permutation, p ≤ q. Lemma 10 ([37]) Let σ be a 1234-avoiding permutation of length n ≥ 0, of parameters (p, ... equation (4). We the electronic journal of combinatorics 9 (2003), #R19 10 2.3 The number of descents and the Tutte polynomial of planar maps A number of refinements...

Ngày tải lên: 07/08/2014, 07:21

... class of binary trees and the set of colored 5-ary trees. The generalization of the parity reversing involution and the bijection to forests of colored binary trees and forests of colored 5-ary trees ... of improper forests of colored binary trees, which reverses the parity of the color numbers of the forests. Hence the right side summand of Formula (1.1) counts t...

Ngày tải lên: 07/08/2014, 15:22

... algebraic proof of a result with the same flavour as the latter: T n+2 (1, −1) = T n (2, −1), where T n (1, −1) has the combinatorial interpretation of being the number of 0–1–2 increasing trees on n ... function of parking functions or the inversion enumerator of labelled trees on n vertices, see [10]. In the following section we prove the main theorem of the paper: ∗ Supporte...

Ngày tải lên: 07/08/2014, 15:22

... the m-dissimilarity vector of T . The set of all m-dissimilarity vectors of phylogenetic trees with n leaves will be called the space of m-dissimilarity vectors of n -trees. Definition 2.7. A metric ... size m and d σ is the total weight of the smallest subtree of T which contains the leaves in σ. By the total weight of a tree, we mean the s um of the weights of all the...

Ngày tải lên: 08/08/2014, 01:20