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 $lceil log_{k} chi(h) rceil$.

In ZF the existence of self-complementary graphs on every infinite set is equivalent to the statement that every infinite set is ’even’. We prove a generalization to k-uniform t-complementary hypergraphs. 1. Self-complementary graphs A graph G is called self-complementary if it is isomorphic to its complement G, which has the same vertices as G and exactly those edges that are not in G. First w...

Given a coloring of the edges of a multi-hypergraph, a rainbow t-matching is a collection of t disjoint edges, each having a different color. In this note we study the problem of finding a rainbow t-matching in an r-partite r-uniform multi-hypergraph whose edges are colored with f colors such that every color class is a matching of size t. This problem was posed by Aharoni and Berger, who asked...

In this paper, we present some studies about relations existing between well known Chomsky string grammars and graph grammars, in particularly hypergraph grammars. We are discussing about deterministic context free Lindenmayer Systems used to describe commands to a device that generates black and white digital images. Instead of well-known methods of drawing, we will paint squares, not lines. A...

We compare tractable classes of constraint satisfaction problems (CSPs). We first give a uniform presentation of the major structural CSP decomposition methods. We then introduce a new class of tractable CSPs based on the concept of hypertree decomposition recently developed in Database Theory. We introduce a framework for comparing parametric decomposition-based methods according to tractabi l...

In this note, we prove that the alternating group A4 is a CI-group and that all disconnected Cayley graphs of A5 are CI-graphs. As a corollary, we conclude that there are exactly 22 non-isomorphic Cayley graphs of A4 • Let G be a finite group and set G# = G \ {I}. For a subset S ~ G# with S = S-l := {S-l Is E S}, the Cayley graph is the graph Cay(G, S) with vertex set G and with x and y adjacen...

Let t ≥ 26 and let F be a k-uniform hypergraph on n vertices. Suppose that |F1∩F2∩F3| ≥ t holds for all F1,F2,F3 ∈F . We prove that the size of F is at most (n−t k−t ) if p = k n satisfies p≤ 2 √ 4t +9−1 and n is sufficiently large. The above inequality for p is best possible.

Let G be an r-uniform hypergraph. The multicolor Ramsey number rk(G) is the minimum n such that every k-coloring of the edges of the complete r-uniform hypergraph K n yields a monochromatic copy of G. Improving slightly upon results from [1], we prove that tk + 1 ≤ rk(K2,t+1) ≤ tk + k + 2, where the lower bound holds when t and k are both powers of a prime p. When t = 1, we improve the lower bo...

A hypergraph H = (V,E) is a subtree hypergraph if there is a tree T on V such that each hyperedge of E induces a subtree of T . To find a minimum size transversal for a subtree hypergraph is, in general, NP-hard. In this paper, we show that if it is possible to decide if a set of vertices W ⊆ V is a transversal in time S(n) ( where n = |V | ), then it is possible to find a minimum size transver...

In k-hypergraph matching, we are given a collection of sets of size at most k, each with an associated weight, and we seek a maximum-weight subcollection whose sets are pairwise disjoint. More generally, in k-hypergraph b-matching, instead of disjointness we require that every element appears in at most b sets of the subcollection. Our main result is a linear-programming based (k − 1 + 1 k )app...