Topics in Discrete Mathematics

Part I. Algebra, Geometry, Numbers

1. Countable Almost Rigid Heyting Algebras
Michael E. Adams, Aleš Pultr

2. Piecewise-Bohr Sets of Integers and Combinatorial Number Theory
Vitaly Bergelson, Hillel Furstenberg, Benjamin Weiss

3. A Generalization of Conway Number Games to Multiple Players
Christopher Cunningham, Igor Kriz

4. Two Isoperimetric Problems for Euclidean Simplices
Miroslav Fiedler

5. On Finitely Generated Varieties of Distributive Double p-algebras and their Subquasivarieties
Václav Koubek, Jirí Sichler

6. The F-triangle of the Generalised Cluster Complex
Christian Krattenthaler

Part II. Ramsey Theory

7. Monochromatic Equilateral Right Triangles on the Integer Grid
Ron Graham, József Solymosi

8. One-sided Coverings of Colored Complete Bipartite Graphs
András Gyárfás, Miklós Ruszinkó, Gábor N. Sárközy, Endre Szemerédi

9. Nonconstant Monochromatic Solutions to Systems of Linear Equations
Neil Hindman, Imre Leader

10. On the Induced Ramsey Number IR(P 3, H)
Alexandr Kostochka, Naeem Sheikh

11. On Explicit Ramsey Graphs and Estimates of the Number of Sums and Products
Pavel Pudlák

Part III. Graphs and Hypergraphs

12. Hereditary Properties of Ordered Graphs
József Balogh, Béla Bollobás, Robert Morris

13. A Proof and Generalizations of the Erdos-Ko-Rado Theorem Using the Method of Linearly Independent Polynomials
Zoltán Füredi, Kyung-Won Hwang, Paul M. Weichsel

14. Unions of Perfect Matchings in Cubic Graphs
Tomáš Kaiser, Daniel Král’, Serguei Norine

15. Random Graphs from Planar and Other Addable Classes
Colin McDiarmid, Angelika Steger, Dominic J. A. Welsh

16. Extremal Hypergraph Problems and the Regularity Method
Brendan Nagle, Vojtech Rödl, Mathias Schacht

Part IV. Homomorphisms

17. Homomorphisms in Graph Property Testing
Noga Alon, Asaf Shapira

18. Counting Graph Homomorphisms
Christian Borgs, Jennifer Chayes, László Lovász, Vera T. Sós, Katalin Vesztergombi

19. Efficient Algorithms for Parameterized H-colorings
Josep Díaz, Maria Serna, Dimitrios M. Thilikos

20. From Graph Colouring to Constraint Satisfaction: There and Back Again
Pavol Hell

Part V. Graph Colorings

21. Thresholds for Path Colorings of Planar Graphs
Glenn G. Chappell, John Gimbel, Chris Hartman

22. Chromatic Numbers and Homomorphisms of Large Girth Hypergraphs
Dwight Duffus, Vojtech Rödl, Bill Sands, Norbert Sauer

23. Acyclic 4-Choosability of Planar Graphs Without Cycles of Specific Lengths
Mickaël Montassier, André Raspaud, Weifan Wang

24. On the Algorithmic Aspects of Hedetniemi’s Conjecture
Claude Tardif

25. Recent Developments in Circular Colouring of Graphs
Xuding Zhu

Part VI. Graph Embeddings

26. Regular Embeddings of Multigraphs
Hubert Fraysseix, Patrice Ossona Mendez

27. Quadrangulations and 5-critical Graphs on the Projective Plane
Bojan Mohar

28. Crossing Number of Toroidal Graphs
János Pach, Géza Tóth

29. Regular Maps on a Given Surface: A Survey
Jozef Širán

30. On Six Problems Posed by Jarik Nešetril
Jørgen Bang-Jensen, Bruce Reed, Mathias Schacht, Robert Šámal, Bjarne Toft, Uli Wagner

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