Ingo Schiermeyer

Bio: Ingo Schiermeyer is an academic researcher from Freiberg University of Mining and Technology. The author has contributed to research in topics: Graph power & Bound graph. The author has an hindex of 25, co-authored 153 publications receiving 2181 citations.

Vertex Colouring and Forbidden Subgraphs – A Survey

Abstract: There is a great variety of colouring concepts and results in the literature. Here our focus is to survey results on vertex colourings of graphs defined in terms of forbidden induced subgraph conditions. Thus, one who wishes to obtain useful results from a graph coloring formulation of his problem must do more than just show that the problem is equivalent to the general problem of coloring a graph. If there is to be any hope, one must also obtain information about the structure of the graphs that need to be colored (D.S. Johnson [66]).

Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles

Abstract: We describe and analyze a ”level-oriented” algorithm, called ”Reverse-Fit”, for packing rectangles into a unit-width, infinite-height bin so as to minimize the total height of the packing. For L an arbitrary list of rectangles, all assumed to have width no more than 1, let h OPT denote the minimum possible bin height within the rectangles in L can be packed, and let RF(L) denote the height actually used by Reverse-Fit. We will show that RF(L)≤2·h OPT for an arbitrary list L of rectangles.

Rainbow Connection in Graphs with Minimum Degree Three

Abstract: An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colours that are needed in order to make G rainbow connected. In this paper we prove that $rc(G) < \frac{3n}{4}$ for graphs with minimum degree three, which was conjectured by Caro et al. [Y. Caro, A. Lev, Y. Roditty, Z. Tuza, and R. Yuster, On rainbow connection, The Electronic Journal of Combinatorics 15 (2008), #57.]

Small Ramsey Numbers

Abstract: We present data which, to the best of our knowledge, includes all known nontrivial values and bounds for specific graph, hypergraph and multicolor Ramsey numbers, where the avoided graphs are complete or complete without one edge. Many results pertaining to other more studied cases are also presented. We give references to all cited bounds and values, as well as to previous similar compilations. We do not attempt complete coverage of asymptotic behavior of Ramsey numbers, but concentrate on their specific values.

Introduction to random graphs

Abstract: From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

Exact algorithms for NP-hard problems: a survey

Abstract: We discuss fast exponential time solutions for NP-complete problems. We survey known results and approaches, we provide pointers to the literature, and we discuss several open problems in this area. The list of discussed NP-complete problems includes the travelling salesman problem, scheduling under precedence constraints, satisfiability, knapsack, graph coloring, independent sets in graphs, bandwidth of a graph, and many more.