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Some duality conjectures for finite graphs and their group theoretic consequences
finite graphs group theoretic consequences
2015/8/26
We pose some graph theoretic conjectures about duality and the diameter of maximal trees in planar graphs, and we describe innovations in the following two topics in Geometric Group Theory, where the ...
Mixing times for random walks on geometric random graphs
Random geometric random graph nodes wireless network model and threshold properties random walk figure d dimension
2015/8/11
A geometric random graph, G^d(n,r), is formed as follows: place n nodes uniformly at random onto the surface of the d-dimensional unit torus and connect nodes which are within a distance r of each oth...
An index formula for simple graphs
Curvature topological invariants graph theory Euler characteristic
2012/5/24
Gauss-Bonnet for simple graphs G assures that the sum of curvatures K(x) over the vertex set V of G is the Euler characteristic X(G). Poincare-Hopf tells that for any injective function f on V the sum...
On rainbow-k-connectivity of random graphs
Rainbow connectivity Random graph Graph algorithms Sharp threshold function Probabilistic method
2012/12/4
A path in an edge-colored graph is called a rainbow path if the edges on it have distinct colors. For k 1, the rainbow-k-connectivity of a graph G, denoted by rck(G), is the minimum number of colors...
Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
Geometric analysis aspects infinite semiplanar graphs nonnegative curvature Metric Geometry
2011/9/6
Abstract: In the present paper, we apply Alexandrov geometry methods to study geometric analysis aspects of infinite semiplanar graphs with nonnegative combinatorial curvature in the sense of Higuchi....
Almost Series-Parallel graphs: structure and colorability
Series-Parallel graphs structure colorability
2011/2/28
The series-parallel (SP) graphs are those containing no topological K4 and are considered trivial.We relax the prohibition distinguishing the SP graphs by forbidding only embeddings of K4 whose edges ...
Contracting planar graphs to contractions of triangulations
planar graph dual graph contraction topological minor
2011/1/20
For every graph H, there exists a polynomial-time algorithm deciding if a planar input graph G can be contracted to H. However, the degree of the polynomial depends on the size of H. In this paper, we...
Generalization of the Bollobás-Riordan polynomial for tensor graphs
(multivariate) topological graph polynomials group eld theory
2011/1/19
Tensor models are used nowadays for implementing a fundamental theory of quan-tum gravity. We de ne here a polynomial T encoding the supplementary topological information.
In this paper we consider the hyperspace Cn(X) of closed, con-nected, non-empty subsets of a base space X. The class of base spaces we consider we call finite ray-graphs, and are a noncompact variatio...
On the heterochromatic number of hypergraphs associated to geometric graphs and to matroids
hypergraphs associated geometric graphs matroids
2010/11/24
The heterochromatic number hc(H) of a non-empty hypergraph H is the smallest integer k such that for every colouring of the vertices of H with exactly k colours, there is a hyperedge of H all of whos...
It has recently been shown that infinite matroids can be axiomatized in a way that is very similar to finite matroids and permits duality. This was previously thought impossible, since finitary infini...
Strongly Regular Graphs Constructed from $p$-ary Bent Functions
Strongly Regular Graphs Constructed math
2010/11/23
In this paper, we generalize the construction of strongly regular graphs in [Y. Tan et al., Strongly regular graphs associated with ternary bent functions, J. Combin.Theory Ser. A (2010), 117, 668-68...
Three-Colorings of Cubic Graphs and Tensor Operators
3-colorings of cubic planar graphs tensor algebras
2010/12/6
Penrose’s work [6] established a connection between the edge 3-colorings of cubic planar graphs and tensor algebras. We exploit this point of view in order to get algebraic representations of the cate...
Drawing planar graphs of bounded degree with few slopes
planar graphs bounded degree few slopes
2010/12/1
settle a problem of Dujmović, Eppstein, Suderman, and Wood by showing that there exists
a function f with the property that every planar graph G with maximum degree d admits a drawing
with nonc...
Edge-intersection graphs of grid paths: the bend-number
Edge-intersection graphs of grid paths bend-number
2010/12/6
We investigate edge-intersection graphs of paths in the plane grid re-garding a parameter called the bend-number. The bend-number is related to the interval-number and the track-number of a graph.