Collineations of the Subiaco generalized quadrangles.
Collisions of random walks
A recurrent graph has the infinite collision property if two independent random walks on , started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton–Watson tree with finite variance conditioned to survive, the incipient infinite cluster in with and the uniform spanning tree in all have the infinite collision property. For power-law combs and spherically symmetric...
Color Energy Of A Unitary Cayley Graph
Let G be a vertex colored graph. The minimum number χ(G) of colors needed for coloring of a graph G is called the chromatic number. Recently, Adiga et al. [1] have introduced the concept of color energy of a graph Ec(G) and computed the color energy of few families of graphs with χ(G) colors. In this paper we derive explicit formulas for the color energies of the unitary Cayley graph Xn, the complement of the colored unitary Cayley graph (Xn)c and some gcd-graphs.
Color neighborhood union conditions for long heterochromatic paths in edge-colored graphs.
Coloration de graphes : fondements et applications
Les modèles classiques de coloration doivent leur notoriété en grande partie à leurs applications à des problèmes de type emploi du temps ; nous présentons les concepts de base des colorations ainsi qu’une série de variations et de généralisations motivées par divers problèmes d’ordonnancement dont les élaborations d’horaires scolaires. Quelques algorithmes exacts et heuristiques seront présentés et nous esquisserons des méthodes basées sur la recherche Tabou pour trouver des solutions approchées...
Coloration de graphes : fondements et applications
The classical colouring models are well known thanks in large part to their applications to scheduling type problems; we describe the basic concepts of colourings together with a number of variations and generalisations arising from scheduling problems such as the creation of school schedules. Some exact and heuristic algorithms will be presented, and we will sketch solution methods based on tabu search to find approximate solutions to large problems. Finally we will also mention the use...
Colorations généralisées, graphes biorientés et deux ou trois choses sur François
La généralisation des nombres chromatiques de Stahl a été un premier thème de travail avec François et a abouti à l’introduction de la notion de colorations généralisées et leurs nombres chromatiques associés, notées . Cette nouvelle notion a permis d’une part, d’infirmer avec Payan une conjecture posée par Brigham et Dutton, et d’autre part, d’étendre de manière naturelle la formule de récurrence de Stahl aux nombres chromatiques . Cette relation s’exprime comme . La conjecture de Bouchet...
Color-bounded hypergraphs, V: host graphs and subdivisions
A color-bounded hypergraph is a hypergraph (set system) with vertex set X and edge set = E₁,...,Eₘ, together with integers and satisfying for each i = 1,...,m. A vertex coloring φ is proper if for every i, the number of colors occurring in edge satisfies . The hypergraph ℋ is colorable if it admits at least one proper coloring. We consider hypergraphs ℋ over a “host graph”, that means a graph G on the same vertex set X as ℋ, such that each induces a connected subgraph in G. In the current...
Colored permutations and skew tableaux. (Permutations colorées et tableaux gauches.)
Colored Prüfer codes for -edge colored trees.
Colored trees and noncommutative symmetric functions.
Coloring digraphs by iterated antichains
We show that the minimum chromatic number of a product of two -chromatic graphs is either bounded by 9, or tends to infinity. The result is obtained by the study of coloring iterated adjoints of a digraph by iterated antichains of a poset.
Coloring of G²∖G, for Euclidesian graph G
Coloring of graphs by partitioning
Coloring rectangular blocks in 3-space
If rooms in an office building are allowed to be any rectangular solid, how many colors does it take to paint any configuration of rooms so that no two rooms sharing a wall or ceiling/floor get the same color? In this work, we provide a new construction which shows this number can be arbitrarily large.
Coloring Some Finite Sets in ℝn
This note relates to bounds on the chromatic number χ(ℝn) of the Euclidean space, which is the minimum number of colors needed to color all the points in ℝn so that any two points at the distance 1 receive different colors. In [6] a sequence of graphs Gn in ℝn was introduced showing that . For many years, this bound has been remaining the best known bound for the chromatic numbers of some lowdimensional spaces. Here we prove that and find an exact formula for the chromatic number in the case of...
Coloring the edges of a random graph without a monochromatic giant component.
Coloring with no 2-colored 's.
Colorings and nowhere-zero flows of graphs in terms of Berlekamp's switching game.
Colorings and orientations of matrices and graphs.