Direction Trees.
Dirichletovy šuplíčky
Článek obsahuje několik příkladů (téměř ze života), jejichž společným jmenovatelem je jednoduchý matematický princip známý jako princip Dirichletův. Hlavním úkolem uvedených příkladů je ilustrovat poněkud překvapivou šíři pole jeho aplikací.
Disconnected neighbourhood graphs
Disconnected vertex sets and equidistant code pairs.
Discovering hook length formulas by an expansion technique.
Discrepancy and eigenvalues of Cayley graphs
We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.
Discrepancy games.
Discrepancy of matrices of zeros ond ones.
Discrepancy of symmetric products of hypergraphs.
Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices
Let be a flat surface of genus with cone type singularities. Given a bipartite graph isoradially embedded in , we define discrete analogs of the Dirac operators on . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair for these discrete Dirac operators to be Kasteleyn matrices of the graph . As a consequence, if these conditions are met, the partition function of the dimer...
Discrete excursions.
Discrete limit laws for additive functions on the symmetric group
Inspired by probabilistic number theory, we establish necessary and sufficient conditions under which the numbers of cycles with lengths in arbitrary sets posses an asymptotic limit law. The approach can be extended to deal with the counts of components with the size constraints for other random combinatorial structures.
Discrete Morse inequalities on infinite graphs.
Discrete n-tuples in Hausdorff spaces
We investigate the following three questions: Let n ∈ ℕ. For which Hausdorff spaces X is it true that whenever Γ is an arbitrary (respectively finite-to-one, respectively injective) function from ℕⁿ to X, there must exist an infinite subset M of ℕ such that Γ[Mⁿ] is discrete? Of course, if n = 1 the answer to all three questions is "all of them". For n ≥ 2 the answers to the second and third questions are the same; in the case n = 2 that answer is "those for which there are only finitely many points...
Discrete polymatroids.
Discrete small world networks.
Discussing graph theory with a computer. II: Theorems suggested by the computer.
Discussing Graph Theory with a Computer III, Man-machine Theorem Proving
Disegni divisibili e loro automorfismi
Disjoint 5-cycles in a graph
We prove that if G is a graph of order 5k and the minimum degree of G is at least 3k then G contains k disjoint cycles of length 5.