Perfect matchings in -regular graphs.
Perfect Set of Euler Tours of Kp,p,p
Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence prove Bermond’s conjecture for G = Kp,p,p.
Perfect transversal in some graph products.
Perfectly balanced partitions of smoothed graphs.
Perfectly matchable subgraph problem on a bipartite graph
We consider the maximum weight perfectly matchable subgraph problem on a bipartite graph G=(UV,E) with respect to given nonnegative weights of its edges. We show that G has a perfect matching if and only if some vector indexed by the nodes in UV is a base of an extended polymatroid associated with a submodular function defined on the subsets of UV. The dual problem of the separation problem for the extended polymatroid is transformed to the special maximum flow problem on G. In this paper, we give...
Permanents, Pfaffian orientations, and even directed circuits.
Permutation separations and complete bipartite factorisations of .
Pfaffian orientation and enumeration of perfect matchings for some Cartesian products of graphs.
Placing bipartite graphs of small size II
In this paper we give all pairs of non mutually placeable (p,q)-bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G)+e(H) ≤ 2p+q-1.
Point partition numbers and generalized Nordhaus-Gaddum problems
Poisson matching
Suppose that red and blue points occur as independent homogeneous Poisson processes in ℝd. We investigate translation-invariant schemes for perfectly matching the red points to the blue points. For any such scheme in dimensions d=1, 2, the matching distance X from a typical point to its partner must have infinite d/2th moment, while in dimensions d≥3 there exist schemes where X has finite exponential moments. The Gale–Shapley stable marriage is one natural matching scheme, obtained by iteratively...
Polynomial-time partition of a graph into cliques.
Primal-dual approximation algorithms for a packing-covering pair of problems
We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and...
Primal-dual approximation algorithms for a packing-covering pair of problems
We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and...
Problem presented at the workshop in Krynica 2004
Problème de la bipartition minimale d'un graphe
Rainbow -factors.
Rainbow -factors of complete -uniform -partite hypergraphs.
Rainbow matching in edge-colored graphs.
Recobriments i grafs distància-regulars.
Uno de los aspectos claves en las telecomunicaciones está relacionado con el uso de los códigos correctores de errores para la transmisión de información. Actualmente se utiliza una clase muy simple de códigos; la implementación física de un código corrector de errores es complicada y costosa. En el campo de la Informática Teórica se intenta abordar el problema de los códigos correctores de errores desde diferentes ángulos. Uno de ellos es el de la Combinatoria Algebraica y, en particular, los grafos...