相关论文: Enumeration of Chord Diagrams without Loops and Pa…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
The Horizontal Chord Theorem states that if a continuous curve connects points $A$ and $B$ in the plane, then for any integer $k$ there are points $C$ and $D$ on the curve such that $\overrightarrow{AB}=k \overrightarrow{CD}$. In this note,…
We call a graph $G$ pancyclic if it contains at least one cycle of every possible length $m$, for $3\le m\le |V(G)|$. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs…
Circuits and extended formulations are classical concepts in linear programming theory. The circuits of a polyhedron are the elementary difference vectors between feasible points and include all edge directions. We study the connection…
The correspondence between monoidal categories and graphical languages of diagrams has been studied extensively, leading to applications in quantum computing and communication, systems theory, circuit design and more. From the categorical…
Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…
We prove that if an $n$-vertex graph with minimum degree at least $3$ contains a Hamiltonian cycle, then it contains another cycle of length $n-o(n)$; this implies, in particular, that a well-known conjecture of Sheehan from 1975 holds…
A caterpillar tree is a connected, acyclic, graph in which all vertices are either a member of a central path, or joined to that central path by a single edge. In other words, caterpillar trees are the class of trees which become path…
We consider a class of "harmonic variations" for nonsingular curves, obtained as asymptotic degenerations along bitangents. On a geometric level, we obtain an attractive relationship between the class and the genus of $C$. The distribution…
Chord diagrams, under the name of Gauss diagrams, are used in low-dimensional topology as an important tool for studying curves or knots. Those Gauss diagrams that correspond to curves or knots are called realizable. The theme of our paper…
A graph $G$ is said to be Hamiltonian if it contains a spanning cycle. In this work, we investigate the Hamiltonian completeness of certain classes of caterpillar graphs, which are trees with a central path to which all other vertices are…
A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no…
Let $P$ be an $x$-monotone orthogonal polygon with $n$ vertices. We call $P$ a simple histogram if its upper boundary is a single edge; and a double histogram if it has a horizontal chord from the left boundary to the right boundary. Two…
We consider the class of graphs containing no odd hole, no odd antihole, and no configuration consisting of three paths between two nodes such that any two of the paths induce a hole, and at least two of the paths are of length 2. This…
A graph is even-hole-free if it has no induced even cycles of length 4 or more. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle. In this paper, we consider (cap, even hole)-free…
We introduce nominal string diagrams as, string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we…
A chord diagram is a circle with paired points with each pair of points connected by a chord. Every generic immersed spherical curve provides a chord diagram by associating each chord with two preimages of a double point. Any two spherical…
We consider the following fundamental realization problem of directed graphs. Given a sequence $S:={a_1 \choose b_1},\dots,{a_n \choose b_n}$ with $a_i,b_i\in \mathbb{Z}_0^+.$ Does there exist a digraph (no loops and no parallel arcs are…
We present an algorithm for enumerating exactly the number of Hamiltonian chains on regular lattices in low dimensions. By definition, these are sets of k disjoint paths whose union visits each lattice vertex exactly once. The well-known…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…