Canonical partition theorems for finite distributive lattices
Capacités de Choquet finies et profinies
On définit les capacités de Choquet dans le cas fini en utilisant une forme bilinéaire non dégénérée associée à la base de Choquet. On montre que, dans le cas fini, une capacité de Choquet est la donnée d’un convexe de mesure qu’on caractérise. Le cas profini, issu des arbres, est obtenu par passage à la limite projective du cas fini. Sur les capacités profinies, on définit une forme bilinéaire dont le rapport avec l’intégration, dans des cas simples, est étudié.
Caractérisation, construction et dénombrement des ultramétriques supérieures minimales
Cardinality of a minimal forbidden graph family for reducible additive hereditary graph properties
An additive hereditary graph property is any class of simple graphs, which is closed under isomorphisms unions and taking subgraphs. Let denote a class of all such properties. In the paper, we consider H-reducible over properties with H being a fixed graph. The finiteness of the sets of all minimal forbidden graphs is analyzed for such properties.
Cardinality of height function’s range in case of maximally many rectangular islands - computed by cuts
We deal with rectangular m×n boards of square cells, using the cut technics of the height function. We investigate combinatorial properties of this function, and in particular we give lower and upper bounds for the number of essentially different cuts. This number turns out to be the cardinality of the height function’s range, in case the height function has maximally many rectangular islands.
Cartesian subdirect irreducibility in graphs
Catalan monoids, monoids of local endomorphisms, and their presentations.
Categorical constructions in graph theory.
Categorification of Hopf algebras of rooted trees
We exhibit a monoidal structure on the category of finite sets indexed by P-trees for a finitary polynomial endofunctor P. This structure categorifies the monoid scheme (over Spec ℕ) whose semiring of functions is (a P-version of) the Connes-Kreimer bialgebra H of rooted trees (a Hopf algebra after base change to ℤ and collapsing H 0). The monoidal structure is itself given by a polynomial functor, represented by three easily described set maps; we show that these maps are the same as those occurring...
Caterpillars
Cayley color graphs of inverse semigroups and groupoids
The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.
Cayley graphs on the symmetric group generated by initial reversals have unit spectral gap.
Centers and centroids of unicyclic graphs
Centers in iterated line graphs.
Centers in line graphs
Centers of directed cacti
Centers of n-fold tensor products of graphs
Formulas for vertex eccentricity and radius for the n-fold tensor product of n arbitrary simple graphs are derived. The center of G is characterized as the union of n+1 vertex sets of form V₁×V₂×...×Vₙ, with .
Centralité et compacité d'un graphe
Un grand nombre de situations de psychologie sociale peuvent être interprétées en termes de graphe, notamment celles qui traitent des phénomènes de relation et de communication. Les travaux de A. Bavelas et H. Leavitt ont révélé l'influence des différents types de réseaux sur le comportement des groupes ; ils ont mis en pleine lumière l'intérêt de la notion de centralité. Les recherches de C. Flament ont enrichi et fortement nuancé ces résultats en faisant apparaître le poids de la nature de la...
Centrally-symmetric tight surfaces and graph embeddings.
Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.