Topics in Discrete Mathematics

This book comprises a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of Professor Jarik NeSetril. Leading experts have contributed survey and research papers in the areas of Algebraic Combinatorics, Combinatorial Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs, Homomorphisms, Graph Colorings and Graph Embeddings.

Résumé

The book offers the readers a collection of high quality papers in selected topics of Discrete Mathematics, to celebrate the 60th birthday of
Professor Jarik Neetril. Leading experts have contributed survey and research
papers in the areas of Algebraic Combinatorics, Combinatorial
Number Theory, Game theory, Ramsey Theory, Graphs and Hypergraphs,
Homomorphisms, Graph Colorings and Graph Embeddings.

Contenu
Algebra, Geometry, Numbers.- Countable Almost Rigid Heyting Algebras.- Piecewise-Bohr Sets of Integers and Combinatorial Number Theory.- A Generalization of Conway Number Games to Multiple Players.- Two Isoperimetric Problems for Euclidean Simplices.- On Finitely Generated Varieties of Distributive Double p-algebras and their Subquasivarieties.- The F-triangle of the Generalised Cluster Complex.- Ramsey Theory.- Monochromatic Equilateral Right Triangles on the Integer Grid.- One-sided Coverings of Colored Complete Bipartite Graphs.- Nonconstant Monochromatic Solutions to Systems of Linear Equations.- On the Induced Ramsey Number IR(P 3, H).- On Explicit Ramsey Graphs and Estimates of the Number of Sums and Products.- Graphs and Hypergraphs.- Hereditary Properties of Ordered Graphs.- A Proof and Generalizations of the Erd?s-Ko-Rado Theorem Using the Method of Linearly Independent Polynomials.- Unions of Perfect Matchings in Cubic Graphs.- Random Graphs from Planar and Other Addable Classes.- Extremal Hypergraph Problems and the Regularity Method.- Homomorphisms.- Homomorphisms in Graph Property Testing.- Counting Graph Homomorphisms.- Efficient Algorithms for Parameterized H-colorings.- From Graph Colouring to Constraint Satisfaction: There and Back Again.- Graph Colorings.- Thresholds for Path Colorings of Planar Graphs.- Chromatic Numbers and Homomorphisms of Large Girth Hypergraphs.- Acyclic 4-Choosability of Planar Graphs Without Cycles of Specific Lengths.- On the Algorithmic Aspects of Hedetniemi's Conjecture.- Recent Developments in Circular Colouring of Graphs.- Graph Embeddings.- Regular Embeddings of Multigraphs.- Quadrangulations and 5-critical Graphs on the Projective Plane.- Crossing Number of Toroidal Graphs.- Regular Maps on a Given Surface: A Survey.-VII.- On Six Problems Posed by Jarik Neet?il.