Title | Combinatorics Advances [electronic resource] / edited by Charles J. Colbourn, Ebadollah S. Mahmoodian |
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Imprint | Boston, MA : Springer US, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-3554-2 |
Descript | XVI, 328 p. online resource |
1 On a Conjecture of A. Hartman -- 1 Notations and Preliminaries -- 2 The Structure of Trades -- 3 Block Size 3 and Strength 2 -- 4 A Possible Approach to the Problem -- 5 The Case of Strength 2 -- 6 Some Examples -- 7 Concluding Remarks -- 2 Some Problems in Total Graph Theory -- 1 Introduction and Preliminaries -- 2 Total Ramsey Numbers -- 3 Vertex Reconstructibility of Total Graphs -- 4 Edge Reconstructibility of Total Graphs -- 5 The Spectrum of Total Graphs -- 6 Groups, and Polynomials of Graphs -- 7 Relationships Between some Parameters of G and those of T(G) -- 8 Some Generalizations and Applications -- 9 Upper Bounds for x? (G) -- 10 Remarks -- 3 Construction Techniques for Mutually Orthogonal Latin Squares -- 1 Background -- 2 History and Small Orders -- 3 Pairwise balanced designs and Greigโs line-flip -- 4 Difference matrices: some direct constructions -- 5 A variant of Wilsonโs theorem -- 6 Concluding remarks -- 4 The Spectrum of R-Orthogonal Latin Squares -- 1 Latin squares and r-orthogonality -- 2 Some basic constructions -- 3 Small sides -- 4 A GDD construction -- 5 Intermediate sides -- 5 General Theory of Translation Invariant Systems -- 1 Introduction -- 2 The Model -- 3 A Residuated Semigroup -- 4 Some Basic Questions -- 6 Some Mathematical Problems Arising in Molecular Bioinformatics: The Concept of Bioinformatics -- 1 Introduction -- 2 The concept of sequence space -- 3 The geometry of sequence space -- 4 Cluster analysis -- 5 Split decomposition -- 6 Concluding remark -- 7 An Algorithmic Approach to Tilings -- 8 A New Connection Between Convex Geometry and Threshold Logic -- 1 Introduction -- 2 Algorithmic Enumeration of Nonisomorphic Cut-Complexes and a Generation of Convex Polytopes -- 3 Geometric Properties -- 9 The Unity of Combinatorics -- 1 Introduction -- 2 Langfordโs Problem -- 3 Skolemโs Problem -- 4 Beatty Sequences -- 5 Penrose Pieces -- 6 Wythoffโs Game -- 7 Triples satisfying x + y = z -- 8 Triples satisfying x + y = 2z -- 9 Coil diagrams -- 10 Squaring the square -- 11 Packing or covering the complete graph -- 12 Hananiโs cyclic Steiner systems -- 13 Perfect difference sets -- 14 Projective planes -- 15 Affine geometries -- 16 Magic squares -- 17 Kirkmanโs schoolgirls problem -- 18 Heawoodโs map on the torus -- 19 The toroidal thickness of the complete graph -- 20 Nim addition -- 21 Incidence matrices -- 22 Zarankiewiczโs problem -- 23 Error-correcting codes -- 24 Hadamard matrices -- 25 Cyclic Hadamard matrices -- 26 Factoring with quadratic forms -- 27 Projective geometries -- 28 Sphere packing -- 29 Mock Turtles -- 10 Unsolved Problems in Combinatorial Games -- 11 (F, 2)โRotational Steiner Triple Systems -- 1 Introduction -- 2 Skolem Sequences -- 3 Constructions -- 4 Main Results -- 12 A Simple Polynomial Time Algorithm for a Convex Hull Problem Equivalent to Linear Programming -- 1 Introduction -- 2 The Algorithm -- 13 A LinearโTime Algorithm for Minimum Cost Flow on Undirected OneโTrees -- 1 Introduction -- 2 The Algorithm -- 14 An Asymptotic Existence Result for Orthogonal Designs -- 1 Introduction -- 2 Basic Results -- 3 Main Results -- 15 Decomposition of Complete Tripartite Graphs Into 5-Cycles -- 1 Introduction -- 2 Necessary Conditions -- 3 An Application -- 4 Sufficiency of Conditions -- 5 Searching for a decomposition in other cases -- 16 The Nsm of a Graph -- 1 The New Stability Measure of a Graph (NSM) -- 2 NSM and Operations on Graphs -- 3 Hamilton Properties of NSM -- 17 Zero-Knowledge Proofs For Independent Set and Dominating Set Problems -- 1 Introduction -- 2 A Zero-Knowledge Proof for Independent set problem -- 3 A Zero-Knowledge Proof for Dominating set problem -- 18 Exploring the Spectrum of Values of Permanents by Simulated Annealing -- 1 The Permanent -- 2 Upper Bounds and Lower Bounds for the Permanent -- 3 Simulated Annealing -- 4 The Metropolis Algorithm -- 5 Results and Conclusions -- 19 VectorโWeighted Matchings -- 1 Introduction -- 2 Preliminaries -- 3 Preference Matchings -- 4 Preference Poly topes -- 5 The Set of Efficient Solutions -- 20 Directed Quadruple Designs -- 1 Introduction -- 2 Existence of 3-(v, 4, l)DDs -- 3 On the Existence of 3-(v, 4, 2)DDs -- 4 Some Small Cases (for ? = 2) -- 21 Bounding Two-Terminal Network Reliability Via Surface Duality -- 1 Introduction -- 2 Definitions -- 3 Results -- 4 Implementation -- 5 Examples -- 22 Defining Sets for Block Designs: An Update -- 1 Introduction -- 2 Some Theoretical Results -- 3 Finding Smallest Defining Sets in Small Designs -- 4 Defining Sets in Some Infinite Classes of Designs -- 23 Open Problems at the Combinatorics Workshop of Aimc25 (Tehran, 1994)