Equitable hypergraph orientations.
Equivalence classes of functions on finite sets.
Equivalence of a Number-Theoretical Problem with a Problem from the Graph Theory
Equivalence of compositional expressions and independence relations in compositional models
We generalize Jiroušek’s (right) composition operator in such a way that it can be applied to distribution functions with values in a “semifield“, and introduce (parenthesized) compositional expressions, which in some sense generalize Jiroušek’s “generating sequences” of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system is star-like with centre if...
Equivalence of the strengthened Hanna Neumann conjecture and the amalgamated graph conjecture.
Equivalences between isomorphism classes on infinite graphs
The paper studies some equivalence relations between isomorphism classes of countable graphs which correspond in a certain sense to various distances between isomorphism classes of finite graphs.
Equivalent classes for K₃-gluings of wheels
In this paper, the chromaticity of K₃-gluings of two wheels is studied. For each even integer n ≥ 6 and each odd integer 3 ≤ q ≤ [n/2] all K₃-gluings of wheels and create an χ-equivalent class.
Erdős regular graphs of even degree
In 1960, Dirac put forward the conjecture that r-connected 4-critical graphs exist for every r ≥ 3. In 1989, Erdös conjectured that for every r ≥ 3 there exist r-regular 4-critical graphs. A method for finding r-regular 4-critical graphs and the numbers of such graphs for r ≤ 10 have been reported in [6,7]. Results of a computer search for graphs of degree r = 12,14,16 are presented. All the graphs found are both r-regular and r-connected.
Erdös-Ko-Rado from intersecting shadows
A set system is called t-intersecting if every two members meet each other in at least t elements. Katona determined the minimum ratio of the shadow and the size of such families and showed that the Erdős-Ko-Rado theorem immediately follows from this result. The aim of this note is to reproduce the proof to obtain a slight improvement in the Kneser graph. We also give a brief overview of corresponding results.
Erdős-Renyi random graphs forest fires self-organized criticality.
Errata: Correction of my paper 'On a problem in map colouring'
Errata : «Les hiérarchies de parties et leur demi-treillis»
Erratum: "Embeddings of 2-spheres in 4-manifolds".
Erratum: Equivalence of compositional expressions and independence relations in compositional models
Erratum to “A note on the largest eigenvalue of non-regular graphs”.
Erratum to : “Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs”
Erratum to the paper "Uniquely edge colourable graph"
Essential self-adjointness for combinatorial Schrödinger operators III- Magnetic fields
We define the magnetic Schrödinger operator on an infinite graph by the data of a magnetic field, some weights on vertices and some weights on edges. We discuss essential self-adjointness of this operator for graphs of bounded degree. The main result is a discrete version of a result of two authors of the present paper.
Establishing Order in Planar Subdivisions.
Estimation of cut-vertices in edge-coloured complete graphs