Using Eulerian cycles construct all graphs with given degree sequence
VŨ ĐINH HÒA
Abstract
A fundamental longstvasting problem of graph theory is to find all graphs whose order is a given sequence of natural numbers. This problem is not only a fundamental theoretical problem, but also a problem that applies in science và practice. The main result of this article is an algorithm based on the concept of balance graphs (which can be constructed using colored Euler cycles) to construct all graphs having a given degree sequence.