Related papers: Pattern avoiding permutations and independent sets…
A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees. In this paper…
We introduce the (private) entropy of a directed graph (in a new network coding sense) as well as a number of related concepts. We show that the entropy of a directed graph is identical to its guessing number and can be bounded from below…
The family of graphs of reduced words of a certain subcollection of permutations in the union $\cup_{n\geq 4}\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with…
We study the problems of counting copies and induced copies of a small pattern graph $H$ in a large host graph $G$. Recent work fully classified the complexity of those problems according to structural restrictions on the patterns $H$. In…
This paper develops two heuristic algorithms to solve graph isomorphism, using free energy encoding. The first algorithm uses four types of encoding refinement techniques such that every graph can be distinguished by a canonical number…
In this paper, we introduce a novel and computationally efficient method for vertex embedding, community detection, and community size determination. Our approach leverages a normalized one-hot graph encoder and a rank-based cluster size…
We show that for any permutation $\pi$ there exists an integer $k_{\pi}$ such that every permutation avoiding $\pi$ as a pattern is a product of at most $k_{\pi}$ separable permutations. In other words, every strict class $\mathcal C$ of…
The stack sort algorithm has been the subject of extensive study over the years. In this paper we explore a generalized version of this algorithm where instead of avoiding a single decrease, the stack avoids a set $T$ of permutations. We…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
Encoding readout methods based on different schemes have been successfully developed and tested with different types of position-sensitive detectors with strip-readout structures. However, how to construct an encoding scheme in a more…
Invertible transformation of large graphs into fixed dimensional vectors (embeddings) remains a challenge. Its overcoming would reduce any operation on graphs to an operation in a vector space. However, most existing methods are limited to…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We study an analogue of the classical moment problem in the framework where moments are indexed by graphs instead of natural numbers. We study limit objects of graph sequences where edges are labeled by elements of a topological space.…
Let $\Delta =\{ \delta_1,\delta_2,...,\delta_m \} $ be a finite set of 2-connected patterns, i.e. graphs up to vertex relabelling. We study the generating function $D_{\Delta }(z,u_1,u_2,...,u_m),$ which counts polygon dissections and marks…
Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable,…
We define strongly chordal digraphs, which generalize strongly chordal graphs and chordal bipartite graphs, and are included in the class of chordal digraphs. They correspond to square 0,1 matrices that admit a simultaneous row and column…
We explore various techniques for counting the number of straight-edge crossing-free graphs that can be embedded on a planar point set. In particular, we derive a lower bound on the ratio of the number of such graphs with $m+1$ edges to the…
This paper follows cognitive studies to investigate a graph representation for sketches, where the information of strokes, i.e., parts of a sketch, are encoded on vertices and information of inter-stroke on edges. The resultant graph…
The study of patterns in permutations in a very active area of current research. Klazar defined and studied an analogous notion of pattern for set partitions. We continue this work, finding exact formulas for the number of set partitions…
Enumeration of pattern-avoiding objects is an active area of study with connections to such disparate regions of mathematics as Schubert varieties and stack-sortable sequences. Recent research in this area has brought attention to colored…