Enumeration of Spanning Subgraphs with Degree Constraints

نویسنده

  • DAVID G. WAGNER
چکیده

For a finite undirected multigraph G = (V, E) and functions f, g : V → N, let N f (G, j) denote the number of (f, g)– factors of G with exactly j edges. The Heilmann-Lieb Theorem implies that ∑ j N 1 0 (G, j)t is a polynomial with only real (negative) zeros, and hence that the sequence N 0 (G, j) is strictly logarithmically concave. Separate generalizations of this theorem were obtained by Ruelle and by the author. We unify, simplify, and generalize these results by means of the Grace–Szegö–Walsh Coincidence Theorem.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weighted enumeration of spanning subgraphs with degree constraints

The Heilmann-Lieb Theorem on (univariate) matching polynomials states that the polynomial ∑ k mk(G)y k has only real nonpositive zeros, in which mk(G) is the number of k-edge matchings of a graph G. There is a stronger multivariate version of this theorem. We provide a general method by which “theorems of Heilmann-Lieb type” can be proved for a wide variety of polynomials attached to the graph ...

متن کامل

The number and degree distribution of spanning trees in the Tower of Hanoi graph

The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of spanning trees and the study of their properties remain a challenge, particularly for large networks. In this paper, we study the number and degree distribut...

متن کامل

Efficient Enumeration of Bipartite Subgraphs in Graphs

Subgraph enumeration problems ask to output all subgraphs of an input graph that belongs to the specified graph class or satisfy the given constraint. These problems have been widely studied in theoretical computer science. As far, many efficient enumeration algorithms for the fundamental substructures such as spanning trees, cycles, and paths, have been developed. This paper addresses the enum...

متن کامل

Distribution of certain sparse spanning subgraphs in random graphs

We describe a general approach of determining the distribution of spanning subgraphs in the random graph G(n, p). In particular, we determine the distribution of spanning subgraphs of certain given degree sequences, which is a generalisation of the d-factors, of spanning trianglefree subgraphs, of (directed) Hamilton cycles and of spanning subgraphs that are isomorphic to a collection of vertex...

متن کامل

Complexity of Computation of a Spanning Tree Enumeration Algorithm

Absrracr -In l!X3, Char [4] presented an algorithm to enumerate all the spanning trees of an undirected graph G. This algorithm starts with a known initial spanning tree of G, and generates all the other spanning trees along with certain spanning non-tree subgraphs of G. In this paper a detailed complexity analysis of char’s algorithm and methods to speed up the algorithm are discussed. Two heu...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004