Related papers: Bijection between oriented maps and weighted non-o…

This paper presents two algorithms. In their simplest form, the first algorithm decides the existence of a pointed homotopy between given simplicial maps f, g from X to Y and the second computes the group $[\Sigma X,Y]^*$ of pointed…

We consider planar bipartite maps which are both tight, i.e. without vertices of degree $1$, and $2b$-irreducible, i.e. such that each cycle has length at least $2b$ and such that any cycle of length exactly $2b$ is the contour of a face.…

Let $I$ and $O$ denote two sets of vertices, where $I\cap O =\emptyset$, $|I| = n$, $|O| = r$, and $B_u(n,r)$ denote the set of unlabeled graphs whose edges connect vertices in $I$ and $O$. Recently, it was established…

In this we consider weighted symmetric digraph. Our result generalizes the work of Zhu (J.Comb.Theory, Ser.B, 86 (2002) 109-113) concerning the (k,d)-coloring of a graph, and thus is also a generalization of a corresponding result of Tuza…

We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.

We introduce the concept of alternate-edge-colourings for maps, and study highly symmetric examples of such maps. Edge-biregular maps of type $(k,l)$ occur as smooth normal quotients of a particular index two subgroup of $T_{k,l}$, the full…

A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…

We introduce jacobian graphs, which are explicit families of regular graphs that are spectrally indistinguishable from random graphs, but whose local structure is very different from that of random graphs. The construction relies on the…

In the class of nonlinear one-parameter real maps we study those with bifurcation that exhibits period doubling cascade. The fixed points of such a map form a finite discrete real set with dimension (2^n)m, where m is the (odd) number of…

The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4, and 2.6), biharmonic maps between…

The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…

An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…

We derive a simple bijection between geometric plane perfect matchings on $2n$ points in convex position and triangulations on $n+2$ points in convex position. We then extend this bijection to monochromatic plane perfect matchings on…

We prove that for every oriented graph $D$ and every choice of positive integers $k$ and $\ell$, there exists an oriented graph $D^*$ along with a surjective homomorphism $\psi\colon V(D^*) \to V(D)$ such that: (i) girth$(D^*) \geq\ell$;…

A bijection is defined from Littlewood-Richardson tableaux to rigged configurations. It is shown that this map preserves the appropriate statistics, thereby proving a quasi-particle expression for the generalized Kostka polynomials, which…

Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric…

A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably…

A permutation is (1-23-4)-avoiding if it contains no four entries, increasing left to right, with the middle two adjacent in the permutation. Here we give a 2-variable recurrence for the number of such permutations, improving on the…

The score of a vertex $x$ in an oriented graph is defined to be its outdegree, \emph{i.e.}, the number of arcs with initial vertex $x$. The score sequence of an oriented graph is the sequence of all scores arranged in nondecreasing order.…