Related papers: Counting Graph Homomorphisms in Bipartite Settings
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
There is a well-known connection between hypergraphs and bipartite graphs, obtained by treating the incidence matrix of the hypergraph as the biadjacency matrix of a bipartite graph. We use this connection to describe and analyse a…
We show that any two Hadamard graphs on the same number of vertices are quantum isomorphic. This follows from a more general recipe for showing quantum isomorphism of graphs arising from certain association schemes. The main result is built…
We show that a simple Markov chain, the Glauber dynamics, can efficiently sample independent sets almost uniformly at random in polynomial time for graphs in a certain class. The class is determined by boundedness of a new graph parameter…
Let $\hom(H,G)$ denote the number of homomorphisms from a graph $H$ to a graph $G$. Sidorenko's conjecture asserts that for any bipartite graph $H$, and a graph $G$ we have $$\hom(H,G)\geq…
The vertex cover problem is a fundamental and widely studied combinatorial optimization problem. It is known that its standard linear programming relaxation is integral for bipartite graphs and half-integral for general graphs. As a…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
Given a graph G, we investigate the question of determining the parity of the number of homomorphisms from G to some other fixed graph H. We conjecture that this problem exhibits a complexity dichotomy, such that all parity graph…
The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J.…
Perfect Matching-Cut is the problem of deciding whether a graph has a perfect matching that contains an edge-cut. We show that this problem is NP-complete for planar graphs with maximum degree four, for planar graphs with girth five, for…
In this paper we are interested in the fine-grained complexity of deciding whether there is a homomorphism from an input graph $G$ to a fixed graph $H$ (the $H$-Coloring problem). The starting point is that these problems can be viewed as…
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement…
The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular…
In the final project paper we consider a graph parameter called readability. Motivation for readability comes from bioinformatics applications. Graphs arising in problems related to genome sequencing are of small readability, which…
Intuitively speaking, a bipartite graph is mirror if it can be drawn in the Cartesian plane in such a way that, the vertices of one stable are points in x=0, the vertices of the other stable set are points in x=1, the edges are straight…
The conjecture of Bollob\'as and Koml\'os, recently proved by B\"ottcher, Schacht, and Taraz [Math. Ann. 343(1), 175--205, 2009], implies that for any $\gamma>0$, every balanced bipartite graph on $2n$ vertices with bounded degree and…
A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…
Various results ensure the existence of large complete bipartite graphs in properly colored graphs when some condition related to a topological lower bound on the chromatic number is satisfied. We generalize three theorems of this kind,…
In this paper we consider the communication problem that involves transmission of correlated sources over broadcast channels. We consider a graph-based framework for this information transmission problem. The system involves a source coding…
There has recently been much progress on exact algorithms for the (un)weighted graph (bi)partitioning problem using branch-and-bound and related methods. In this note we present and improve an easily computable, purely combinatorial lower…