Embedding a forest in a graph.
Embedding graphs in their complements
Embeddings of Graphs in Euclidean Spaces.
Endlichkeitssätze für k-kritische Graphen.
Enumerating all Hamilton cycles and bounding the number of Hamilton cycles in 3-regular graphs.
Énumération des chemins -minimum admissibles entre deux points
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.
Erratum to “A note on the largest eigenvalue of non-regular graphs”.
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.
Evolutionary families of sets.
Exklusive Graphen und Hamiltonsche Graphen n-ten Grades I.
Exklusive Graphen und Hamiltonsche Graphen n-ten Grades II.
Explicit Ramsey graphs and Erdős distance problems over finite Euclidean and non-Euclidean spaces.
Explicit Ramsey graphs and orthonormal labelings.
Extending the MAX Algorithm for Maximum Independent Set
The maximum independent set problem is an NP-hard problem. In this paper, we consider Algorithm MAX, which is a polynomial time algorithm for finding a maximal independent set in a graph G. We present a set of forbidden induced subgraphs such that Algorithm MAX always results in finding a maximum independent set of G. We also describe two modifications of Algorithm MAX and sets of forbidden induced subgraphs for the new algorithms.
Extremal bipartite graphs with a unique k-factor
Given integers p > k > 0, we consider the following problem of extremal graph theory: How many edges can a bipartite graph of order 2p have, if it contains a unique k-factor? We show that a labeling of the vertices in each part exists, such that at each vertex the indices of its neighbours in the factor are either all greater or all smaller than those of its neighbours in the graph without the factor. This enables us to prove that every bipartite graph with a unique k-factor and maximal size...
Extremal Crossing Numbers of Complete -Chromatic Graphs
Extremal graph theory for metric dimension and diameter.
Extremal Matching Energy of Complements of Trees
Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have...