Flexible color lists in Alon and Tarsi's theorem, and time scheduling with unreliable participants.
Flows on the join of two graphs
The join of two graphs and is a graph formed from disjoint copies of and by connecting each vertex of to each vertex of . We determine the flow number of the resulting graph. More precisely, we prove that the join of two graphs admits a nowhere-zero -flow except for a few classes of graphs: a single vertex joined with a graph containing an isolated vertex or an odd circuit tree component, a single edge joined with a graph containing only isolated edges, a single edge plus an isolated...
Folding on the wedge sum of graphs and their fundamental group.
Fonctions symétriques associées à des suites classiques de nombres
Fonctions symétriques et séries hypergéométriques basiques multivariées
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...
For which graphs does every edge belong to exactly two chordless cycles?
Forbidden configurations: exact bounds determined by critical substructures.
Forbidden Structures for Planar Perfect Consecutively Colourable Graphs
A consecutive colouring of a graph is a proper edge colouring with posi- tive integers in which the colours of edges incident with each vertex form an interval of integers. The idea of this colouring was introduced in 1987 by Asratian and Kamalian under the name of interval colouring. Sevast- janov showed that the corresponding decision problem is NP-complete even restricted to the class of bipartite graphs. We focus our attention on the class of consecutively colourable graphs whose all induced...
Forbidden Subgraphs for Hamiltonicity of 1-Tough Graphs
A graph G is said to be 1-tough if for every vertex cut S of G, the number of components of G − S does not exceed |S|. Being 1-tough is an obvious necessary condition for a graph to be hamiltonian, but it is not sufficient in general. We study the problem of characterizing all graphs H such that every 1-tough H-free graph is hamiltonian. We almost obtain a complete solution to this problem, leaving H = K1 ∪ P4 as the only open case.
Forbidden triples implying Hamiltonicity: for all graphs
In [2], Brousek characterizes all triples of graphs, G₁, G₂, G₃, with for some i = 1, 2, or 3, such that all G₁G₂G₃-free graphs contain a hamiltonian cycle. In [6], Faudree, Gould, Jacobson and Lesniak consider the problem of finding triples of graphs G₁, G₂, G₃, none of which is a , s ≥ 3 such that G₁, G₂, G₃-free graphs of sufficiently large order contain a hamiltonian cycle. In this paper, a characterization will be given of all triples G₁, G₂, G₃ with none being , such that all G₁G₂G₃-free...
Forbidden-minor characterization for the class of cographic element splitting matroids
In this paper, we prove that an element splitting operation by every pair of elements on a cographic matroid yields a cographic matroid if and only if it has no minor isomorphic to M(K₄).
Forbidden-minor characterization for the class of graphic element splitting matroids
This paper is based on the element splitting operation for binary matroids that was introduced by Azadi as a natural generalization of the corresponding operation in graphs. In this paper, we consider the problem of determining precisely which graphic matroids M have the property that the element splitting operation, by every pair of elements on M yields a graphic matroid. This problem is solved by proving that there is exactly one minor-minimal matroid that does not have this property.
Forest decompositions of graphs with cyclomatic number 2.
Forest decompositions of graphs with cyclomatic number 3.
Forestation in hypergraphs: Linear -trees.
Formal calculus and umbral calculus.
Formulas for sums of powers of integers by functional equations.
Forte connexité des complexes polyèdraux
Four classes of pattern-avoiding permutations under one roof: Generating trees with two labels.