Add to ORKGThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 60-62).We give nontrivial upper and lower bounds for the total number of distinct degree sequences among all simple, unlabeled graphs on n vertices (graphical partitions on n vertices). Our upper bound is ... for some constant C, and improvement of ... over the trivial upper bound which is asymptotic to ... Our lower bound is ..., and improvement of ... over the trivial lower bound which is asymptotic to ...by Jason Matthew Burns.Ph.D
summary:We give a necessary and sufficient condition for the existence of a tree of order $n$ with a...
Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwi...
In this work we determine the expected number of vertices of degree k = k(n) in a graph with n verti...
A graph consists of vertices and edges, connecting pairs of vertices. The subject of graph generatio...
In the paper we report on the parallel enumeration of the degree sequences (their number is denoted ...
This dissertation focuses on the intersection of two classical and fundamental areas in graph theory...
We consider the estimation of the number of labelled simple graphs with degree sequence d1, d2, . . ...
The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order....
The Erdős–Gallai criteria for recognizing degree sequences of simple graphs involve a system of ineq...
This paper addresses the classical problem of characterizing degree sequences that can be realized b...
AbstractThe paper sets out to investigate the degree sequences d1⩾d2⩾…⩾dn of random graphs of order ...
We prove that the degree 4 sum-of-squares (SOS) relaxation of the clique number of the Paley graph o...
AbstractWei discovered that the stability number, α(G), of a graph, G, with degree sequence d1, d2,…...
We present an algorithm to test whether a given graphical degree sequence is forcibly connected or n...
A sequence d = (d1, d2, …, dn) of integers is a degree sequence if there exists a (simple) graph G s...
summary:We give a necessary and sufficient condition for the existence of a tree of order $n$ with a...
Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwi...
In this work we determine the expected number of vertices of degree k = k(n) in a graph with n verti...
A graph consists of vertices and edges, connecting pairs of vertices. The subject of graph generatio...
In the paper we report on the parallel enumeration of the degree sequences (their number is denoted ...
This dissertation focuses on the intersection of two classical and fundamental areas in graph theory...
We consider the estimation of the number of labelled simple graphs with degree sequence d1, d2, . . ...
The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order....
The Erdős–Gallai criteria for recognizing degree sequences of simple graphs involve a system of ineq...
This paper addresses the classical problem of characterizing degree sequences that can be realized b...
AbstractThe paper sets out to investigate the degree sequences d1⩾d2⩾…⩾dn of random graphs of order ...
We prove that the degree 4 sum-of-squares (SOS) relaxation of the clique number of the Paley graph o...
AbstractWei discovered that the stability number, α(G), of a graph, G, with degree sequence d1, d2,…...
We present an algorithm to test whether a given graphical degree sequence is forcibly connected or n...
A sequence d = (d1, d2, …, dn) of integers is a degree sequence if there exists a (simple) graph G s...
summary:We give a necessary and sufficient condition for the existence of a tree of order $n$ with a...
Recently, Barabási and Albert [2] suggested modeling complex real-world networks such as the worldwi...
In this work we determine the expected number of vertices of degree k = k(n) in a graph with n verti...