An Efficient Algorithm to Generate all Labeled Triangle-free Graphs with a given Graphical Degree Sequence

TL;DR

The paper presents an efficient, extendable algorithm for generating all labeled triangle-free graphs with a specified degree sequence, avoiding exhaustive enumeration and enabling parallelization.

Contribution

It introduces a novel pruning-based algorithm that efficiently generates all such graphs and can be extended to bipartite graphs, improving over previous methods.

Findings

Efficient generation of all labeled triangle-free graphs for a given degree sequence.

Algorithm can be extended to generate bipartite graphs with the same degree constraints.

The method is suitable for parallel implementation.

Abstract

We extend our previous algorithm that generates all labeled graphs with a given graphical degree sequence to generate all labeled triangle-free graphs with a given graphical degree sequence. The algorithm uses various pruning techniques to avoid having to first generate all labeled realizations of the input sequence and then testing whether each labeled realization is triangle-free. It can be further extended to generate all labeled bipartite graphs with a given graphical degree sequence by adding a simple test whether each generated triangle-free realization is a bipartite graph. All output graphs are generated in the lexicographical ordering as in the original algorithm. The algorithms can also be easily parallelized.