相关论文: Euler-genus distributions of cubic Halin graphs
Enumerating bicolored maps and maps according to the numbers (and possibly types) of edges, faces, white vertices, black vertices and genus has been an important topic arising in many fields of mathematics and physics. In particular,…
When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…
We present fast and efficient randomized distributed algorithms to find Hamiltonian cycles in random graphs. In particular, we present a randomized distributed algorithm for the $G(n,p)$ random graph model, with number of nodes $n$ and…
The generalized Dehn-Sommerville relations determine the odd subalgebra of the combinatorial Hopf algebra. We introduce a class of eulerian hypergraphs that satisfy the generalized Dehn-Sommerville relations for the combinatorial Hopf…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…
We discuss some natural maps from a unitary group U(n) to a smaller group U(n-m) (these maps are versions of the Livshic characteristic function). We calculate explicitly the direct images of the Haar measure under some maps. We evaluate…
We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by projecting to the x-line or Kummer surface, where we can…
We obtain a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. We obtain counterexamples to…
We obtain a recurrence relation for the f-polynomial of Gelfand-Zetlin polytopes by analyzing geometric properties of a linear projection of the Gelfand-Zetlin polytope onto a cube. We apply this recurrence relation to find explicit…
For each commutative, graded algebra with finite dimension in each degree, we construct a graded cohomology theory for graphs whose graded Euler characteristic is the chromatic polynomial of the graph. This extends our previous work which…
We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…
Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of…
The central idea of this article is to present a systematic approach to construct some recurrence relations for the solutions of the second-order linear difference equation of hypergeometric-type defined on the quadratic-type lattices. We…
For $p,q\ge2$ the $\{p,q\}$-tiling graph is the (finite or infinite) planar graph $T_{p,q}$ where all faces are cycles of length $p$ and all vertices have degree $q$. We give algorithms for the problem of recognizing (induced) subgraphs of…
Back in the Eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the…
We provide an algorithm for computing the Euler characteristic of the curves $S_p$ in the space of cubic polynomials, consisting of all polynomials with a periodic critical point of period $p$. The curves were introduced in [Milnor,…
The combinatorial Hopf algebra on building sets $BSet$ extends the chromatic Hopf algebra of simple graphs. The image of a building set under canonical morphism to quasi-symmetric functions is the chromatic symmetric function of the…
We derive an exact closed-form analytical expression for the distribution of the cover time for a random walk over an arbitrary graph. In special case, we derive simplified exact expressions for the distributions of cover time for a…
The genus of a graph is a topological invariant that measures the minimum genus of a surface on which the graph can be embedded without any edges crossing. Graph genus plays a fundamental role in topological graph theory, used to classify…