# Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity

**Edited By**

- J. Nešetřil, Department of Applied Mathematics, Charles University, Prague, Czechoslovakia
- M. Fiedler, Mathematics Institute, Czechoslovak Academy of Science, Prague, Czechoslovakia

This volume in the Annals of Discrete Mathematics brings together contributions by renowned researchers in combinatorics, graphs and complexity. The conference on which this book is based was the fourth in a series which began in 1963, which was the first time specialists from East and West were able to come together. The 1990 meeting attracted 170 mathematicians and computer scientists from around the world, so this book represents an international, detailed view of recent research.

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Published: June 1992

Imprint: North-holland

ISBN: 978-0-444-89543-1

## Contents

- Two Sequences of 2-Regular Graceful Graphs Consisting of 4-gons (J. Abrham, A. Kotzig†). A Survey of Self-Dual Polyhedra (D. Archdeacon). On Magic Labellings of Convex Polytopes (M. Bača). A Packing Problem and Geometrical Series (V. Bálint). On the Bananas Surface B2 (R. Bodendiek, K. Wagner). Structural Properties and Colorings of Plane Graphs (O.V. Borodin). The Binding Number of Graphs (M. Borowiecki). Note on Algorithmic Solvability of Trahtenbrot-Zykov Problem (P. Bugata). Cartesian Dimensions of a Graph (G. Burosch, P. V. Ceccherini). The Steiner Minimal Tree Problem in L2p (D. Cieslik). On k-Connected Subgraphs of the Hypercube (T. Dvořák). On Some of My Favourite Problems in Various Branches of Combinatorics (P. Erdös). Realizability of Some Starlike Trees (D. Fronček). The Construction of All Configurations (124, 163) (H. Gropp). (
p,q )-realizability of Integer Sequences with Respect to Möbius Strip (M. Horňák). Vertex Location Problems (O. Hudec). On Generation of a Class of Flowgraphs (A.J.C. Hurkens, C.A.J. Hurkens, R.W. Whitty). The Weight of a Graph (J. Ivančo). On the Kauffman Polynomial of Planar Matroids (F. Jaeger). On Symmetry Groups of Selfdual Convex Polyhedra (S. Jendrol). A Remark on 2- (&ugr;,&kgr;,&lgr;) Designs (V. Jurák). On a New Class of Intersection Graphs (M. Koebe). Asymptotic Normality of Isolated Edges in Random Subgraphs of the n-Cube (U. Konieczna). On Bounds of the Bisection Width of Cubic Graphs (A.V. Kostochka, L.S. Mel'nikov). On Random Cubical Graphs (A.V. Kostochka, A.A. Sapozhenko, K. Weber). On the Computational Complexity of Seidel's Switching (J. Kratochvíl, J. Nešetřil, O. Zýka). The Harmonious Chromatic Number of a Graph (A. Kundrík). Arboricity and Star Arboricity of Graphs (A. Kurek). Extended 4-Profiles of Hadamard Matrices (C. Lin, W.D. Wallis, Z. Lie). Good Family Packing (M. Loebl, S. Poljak). Solution of an Extremal Problem Concerning Edge-Partitions of Graphs (Z. Lonc). Balanced Extensions of Spare Graphs (T. Luczak, A. Ruciński). Two Results on Antisocial Families of Balls (A. Malnič, B. Mohar). Hamiltonicity of Vertex-transitive pq-Graphs (D. Marušič). On Nodes of Given Out-Degree in Random Trees (A. Meir, J.W. Moon). All Leaves and Excesses are Realizable for k=3 and All &lgr; (E. Mendelsohn, N. Shalaby, S. Hao). The Binding Number of k-Trees (D. Michalak). An Extension of Brook's Theorem (P. Mihók). On Sectors in a Connected Graph (L. Nebeský). Irreconstructability of Finite Undirected Graphs from Large Subgraphs (V. Nýdl). On Inefficient Proofs of Existence and Complexity Classes (C.H. Papadimitriou). Optimal Coteries on a Network (C.H. Papadimitriou, M. Sideri). On Some Heuristics for the Steiner Problem in Graphs (J. Plesník). Minimax Results and Polynomial Algorithms in VLSI Routing (A. Recski). Critical Perfect Systems of Difference Sets (D.G. Rogers). Some Operations (Not) Preserving the Integer Rounding Property (A. Rycerz). Optimal Embedding of a Tree into an Interval Graph in Linear Time (P. Scheffler). Construction of Polytopal Graphs (W. Schöne). More About Two-Graphs (J.J. Seidel). These are the Two-free Trees (J. Sheehan, C.R.J. Clapham). A Note on Reconstructing the Characteristic Polynomial of a Graph (S.K. Simić). Exponential Constructions of Some Nonhamiltonian Minima (Z. Skupień). Hamiltonicity of Products of Hypergraphs (M. Sonntag). Non-Hamiltonian Simple 3-Polytopal Graphs with Edges of Only Two Types (M. Tkáč). On Spectra of Trees and Related Two-Graphs (S.V. Tsaranov). Metrically Regular Square of Metrically Regular Bigraphs (V. Vetchý). Embedding of Graphs in the Complements of Their Squares (M. Wozniak). An 11/6-Approximation Algorithm for the Steiner Problem on Graphs (A.Z. Zelikovsky). The Space of Graphs and its Factorizations (A.A. Zykov). Problems Proposed at the Problem Session of the Prachatice Conference on Graph Theory. Index.