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
Estimation of the index of
Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.
Estrada index of iterated line graphs
Eternal Domination: Criticality and Reachability
We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached. The study of the stronger assertion that such a set can be reached after a single attack is defended leads to the study of graphs which are critical in the sense that deleting any vertex reduces the eternal domination number. Examples of these graphs and tight...
Etude du spectre pour certains noyaux sur un arbre
Etude sur les plans en blocs incomplets equilibres
Eulerian polar graphs
Euler's idoneal numbers and an inequality concerning minimal graphs with a prescribed number of spanning trees
Let be the least number for which there exists a simple graph with vertices having precisely spanning trees. Similarly, define as the least number for which there exists a simple graph with edges having precisely spanning trees. As an -cycle has exactly spanning trees, it follows that . In this paper, we show that and if and only if , which is a subset of Euler’s idoneal numbers. Moreover, if and we show that and This improves some previously estabilished bounds.
Evaluating a weighted graph polynomial for graphs of bounded tree-width.