منابع مشابه
Pattern Hypergraphs
The notion of pattern hypergraph provides a unified view of several previously studied coloring concepts. A pattern hypergraph H is a hypergraph where each edge is assigned a type Πi that determines which of possible colorings of the edge are proper. A vertex coloring of H is proper if it is proper for every edge. In general, the set of integers k such that H can be properly colored with exactl...
متن کاملCounting Pattern-free Set Partitions II: Noncrossing and Other Hypergraphs
A (multi)hypergraph H with vertices in N contains a permutation p = a1a2 . . . ak of 1, 2, . . . , k if one can reduce H by omitting vertices from the edges so that the resulting hypergraph is isomorphic, via an increasing mapping, to Hp = ({i, k + ai} : i = 1, . . . , k). We formulate six conjectures stating that if H has n vertices and does not contain p then the size of H is O(n) and the num...
متن کاملLossy Compression of Pattern Databases Using Acyclic Random Hypergraphs
A domain-independent heuristic function created by an abstraction is usually implemented using a Pattern Database (PDB), which is a lookup table of (abstract state, heuristic value) pairs. PDBs containing high quality heuristic values generally require substantial memory space and therefore need to be compressed. In this paper, we introduce Acyclic Random Hypergraph Compression (ARHC), a domain...
متن کاملdecomposing hypergraphs into k-colorable hypergraphs
for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.
متن کاملDirected domination in oriented hypergraphs
ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2010
ISSN: 1077-8926
DOI: 10.37236/287