Finite commutative monoids of open maps
Finite graphs and digraphs which are not reconstructible from their cardinality restricted subgraphs
Flexible color lists in Alon and Tarsi's theorem, and time scheduling with unreliable participants.
Food Webs, Competition Graphs, and Habitat Formation
One interesting example of a discrete mathematical model used in biology is a food web. The first biology courses in high school and in college present the fundamental nature of a food web, one that is understandable by students at all levels. But food webs as part of a larger system are often not addressed. This paper presents materials that can be used in undergraduate classes in biology (and mathematics) and provides students with the opportunity...
From factorizations of noncommutative polynomials to combinatorial topology
This is an extended version of a talk given by the author at the conference “Algebra and Topology in Interaction” on the occasion of the 70th Anniversary of D.B. Fuchs at UC Davis in September 2009. It is a brief survey of an area originated around 1995 by I. Gelfand and the speaker.
Frucht’s Theorem for the Digraph Factorial
To every graph (or digraph) A, there is an associated automorphism group Aut(A). Frucht’s theorem asserts the converse association; that for any finite group G there is a graph (or digraph) A for which Aut(A) ∼= G. A new operation on digraphs was introduced recently as an aid in solving certain questions regarding cancellation over the direct product of digraphs. Given a digraph A, its factorial A! is certain digraph whose vertex set is the permutations of V (A). The arc set E(A!) forms a group,...
Fundamental groupoids of -graphs.
Game colouring directed graphs.
General numeration II. Division schemes.
This is the second in a series of two papers on numeration schemes. Whereas the first paper emphasized grouping as exemplified in the partition of a number so as to obtain its base two numeral, the present paper takes at its point of departure the method of repeated divisions, as in the calculation of the base two numeral for a number by dividing it by two, then dividing the quotient by two, etc., and collecting the remainders. This method is a sort of classification scheme - odd or even.
Generalizations Of A Reccurence Relation For The Characteristic Polynomials Of Trees
Generalized indices of Boolean matrices
We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.
Generalized uniformly line vulnerable digraphs
Geography played on an -cycle times a 4-cycle.
Graph isomorphisms of partially ordered sets
Graphs and associative triples in quasitrivial groupoids
Graphs associated with nilpotent Lie algebras of maximal rank.
In this paper, we use the graphs as a tool to study nilpotent Lie algebras. It implies to set up a link betwcen graph theory and Lie theory. To do this, it is already known that every nilpotent Lie algebra of maximal rank is associated with a generalized Cartan matrix A and it ils isomorphic to a quotient of the positive part n+ of the KacMoody algebra g(A). Then, if A is affine, we can associate n+ with a directed graph (from now on, we use the term digraph) and we can also associate a subgraph...
Graphs of semigroups
Groupoids with non-associative triples on the diagonal
Hall exponents of matrices, tournaments and their line digraphs
Let be a square -matrix. Then is a Hall matrix provided it has a nonzero permanent. The Hall exponent of is the smallest positive integer , if such exists, such that is a Hall matrix. The Hall exponent has received considerable attention, and we both review and expand on some of its properties. Viewing as the adjacency matrix of a digraph, we prove several properties of the Hall exponents of line digraphs with some emphasis on line digraphs of tournament (matrices).
Hamiltonian circuits in cubic graphs