Related papers: Towards Constructing Ramanujan Graphs Using Shift …
The cut polytope of a graph arises in many fields. Although much is known about facets of the cut polytope of the complete graph, very little is known for general graphs. The study of Bell inequalities in quantum information science…
A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism.…
Twin-width is a recently formulated graph and matrix invariant that intuitively quantifies how far a graph is from having the structural simplicity of a co-graph. Since its introduction in 2020, twin-width has received increasing attention…
For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths…
In this note, we prove that every graph obtained from a bipartite graph by iteratively splitting vertices into two adjacent twins has the de Bruijn-Erd\H{o}s property.
This paper develops an algorithm that identifies and decomposes a median graph of a triangulation of a 2-dimensional (2D) oriented bordered surface and in addition restores all corresponding triangulation whenever they exist. The algorithm…
Recently Friedman proved Alon's conjecture for many families of d-regular graphs, namely that given any epsilon > 0 `most' graphs have their largest non-trivial eigenvalue at most 2 sqrt{d-1}+epsilon in absolute value; if the absolute value…
Dujmovi\'c et al (FOCS2019) recently proved that every planar graph $G$ is a subgraph of $H\boxtimes P$, where $\boxtimes$ denotes the strong graph product, $H$ is a graph of treewidth 8 and $P$ is a path. This result has found numerous…
We study the problem of finding a minimum $k$-critical-bipartite graph of order $(n,m)$: a bipartite graph $G=(U,V;E)$, with $|U|=n$, $|V|=m$, and $n>m>1$, which is $k$-critical-bipartite, and the tuple $(|E|, \Delta_U, \Delta_V)$, where…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
We describe how the Hardy-Ramanujan-Rademacher formula can be implemented to allow the partition function $p(n)$ to be computed with softly optimal complexity $O(n^{1/2+o(1)})$ and very little overhead. A new implementation based on these…
We consider space efficient implementations of some classical applications of DFS including the problem of testing biconnectivity and $2$-edge connectivity, finding cut vertices and cut edges, computing chain decomposition and…
A "book" with k pages consists of a straight line (the "spine") and k half-planes (the "pages"), such that the boundary of each page is the spine. If a graph is drawn on a book with k pages in such a way that the vertices lie on the spine,…
Although research on the control of networked systems has grown considerably, graph-theoretic and algorithmic studies on matrix-weighted graphs remain limited. To bridge this gap in the literature, this work introduces two algorithms-the…
Expander graphs, due to their mixing properties, are useful in many algorithms and combinatorial constructions. One can produce an expander graph with high probability by taking a random graph (e.g., the union of $d$ random bijections for a…
Sparse neural networks are shown to give accurate predictions competitive to denser versions, while also minimizing the number of arithmetic operations performed. However current hardware like GPU's can only exploit structured sparsity…
In earlier papers, we showed a decomposition of the arcs of 2-diregular digraphs (2-dds) and used it to prove some conditions for these graphs to be non-Hamiltonian; we then extended this decomposition to a larger class of digraphs and used…
Local search is a widely-employed strategy for finding good solutions to Traveling Salesman Problem. We analyze the problem of determining whether the weight of a given cycle can be decreased by a popular $k$-opt move. Earlier work has…
We consider the maximum vertex-weighted matching problem (MVM) for non-bipartite graphs. In earlier work we have described a 2/3-approximation algorithm for the MVM on bipartite graphs (Dobrian, Halappanavar, Pothen and Al-Herz, SIAM J.…
We give a Python program that is capable to compute and print all the distinct trivalent 2-stratifold graphs up to $N$ white vertices with trivial fundamental group. Our algorithm uses the three basic operations to construct new graphs from…