Results 21 to 30 of about 9,193,291 (353)
Asymptotic enumeration of digraphs and bipartite graphs by degree sequence [PDF]
We provide asymptotic formulae for the numbers of bipartite graphs with given degree sequence, and of loopless digraphs with given in‐ and out‐degree sequences, for a wide range of parameters including the biregular case.
Anita Liebenau, N. Wormald
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Hamiltonian degree sequences in digraphs
We show that for each >0 every digraph G of sufficiently large order n is Hamiltonian if its out- and indegree sequences d^+_1\le ... \le d^+_n and d^- _1 \le ... \le d^-_n satisfy (i) d^+_i \geq i+ n or d^-_{n-i- n} \geq n-i and (ii) d^-_i \geq i+ n or d^+_{n-i- n} \geq n-i for all i < n/2.
Daniela Kühn+2 more
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The degree sequence on tensor and cartesian products of graphs and their omega index
The aim of this paper is to illustrate how degree sequences may successfully be used over some graph products. Moreover, by taking into account the degree sequence, we will expose some new distinguishing results on special graph products.
Bao-Hua Xing+2 more
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An extremal problem on potentially K_p,1,1-graphic sequences [PDF]
A sequence S is potentially K_p,1,1 graphical if it has a realization containing a K_p,1,1 as a subgraph, where K_p,1,1 is a complete 3-partite graph with partition sizes p,1,1.
Chunhui Lai
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Let G(V,X) be a finite and simple graph of order n and size m. The complement of G, denoted by G¯, is the graph obtained by removing the lines of G and adding the lines that are not in G.
Amrithalakshmi Pai+4 more
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The polytope of degree sequences of hypergraphs
AbstractLet Dn(r) denote the convex hull of degree sequences of simple r-uniform hypergraphs on the vertex set {1,2,…,n}. The polytope Dn(2) is a well-studied object. Its extreme points are the threshold sequences (i.e., degree sequences of threshold graphs) and its facets are given by the Erdös–Gallai inequalities. In this paper we study the polytopes
N. L. Bhanu Murthy, Murali K. Srinivasan
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On degree sequence optimization [PDF]
We consider the problem of finding a subgraph of a given graph which maximizes a given function evaluated at its degree sequence. While the problem is intractable already for convex functions, we show that it can be solved in polynomial time for convex multi-criteria objectives.
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Packing Tree Degree Sequences [PDF]
AbstractA degree sequence is a list of non-negative integers, $${D = d_1, d_2, \ldots , d_n}$$D=d1,d2,…,dn. It is called graphical if there exists a simple graph G such that the degree of the ith vertex is $$d_i$$di; G is then said to be a realization of D. A tree degree sequence is one that is realized by a tree.
Bérczi, Kristóf+3 more
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A General Computational Approach for Counting Labeled Graphs
This paper presents a general recursive formula to estimate the number of labeled graphs as well as details to evaluate the formula for the following graph properties: number of edges (graph density), degree sequence, degree distribution, classification ...
Ravi Goyal, Victor De Gruttola
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The Random Plots Graph Generation Model for Studying Systems with Unknown Connection Structures
We consider the problem of modeling complex systems where little or nothing is known about the structure of the connections between the elements. In particular, when such systems are to be modeled by graphs, it is unclear what vertex degree distributions
Evgeny Ivanko, Mikhail Chernoskutov
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