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1.
Siberian Mathematical Journal - Let $ \{(A_{i},B_{i})\}_{i=1}^{m} $ be a set pair system. Füredi, Gyárfás, and Király called it $ 1 $ -cross intersecting if $... 相似文献
2.
For every ?>0 and every positive integers Δ and r, there exists C=C(?,Δ,r) such that the Ramsey number, R(H,H) of any r-uniform hypergraph H with maximum degree at most Δ is at most C|V(H)|1+?. 相似文献
3.
Alexandr V. Kostochka 《Combinatorica》2002,22(2):275-285
Dedicated to the memory of Paul Erdős
Let f(r,p,t) (p > t >= 1, r >= 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f(r,p,2) for p = 3, 4, 5, 6 were found in [1] and bounds on f(r,7,2) are given in [3]. Here we prove that for large p and huge r.
Received September 23, 1999
RID="*"
ID="*" This work was partially supported by the grant 99-01-00581 of the Russian Foundation for Fundamental Research and the
Dutch–Russian Grant NWO-047-008-006. 相似文献
4.
Let be a hypergraph. A panchromatic t-colouring of is a t-colouring of its vertices such that each edge has at least one vertex of each colour; and is panchromatically t-choosable if, whenever each vertex is given a list of t colours, the vertices can be coloured from their lists in such a way that each edge receives at least t different colours. The Hall ratio of is . Among other results, it is proved here that if every edge has at least t vertices and whenever , then is panchromatically t-choosable, and this condition is sharp; the minimum such that every t-uniform hypergraph with is panchromatically t-choosable satisfies ; and except possibly when t = 3 or 5, a t-uniform hypergraph is panchromatically t-colourable if whenever , and this condition is sharp. This last result dualizes to a sharp sufficient condition for the chromatic index of a hypergraph
to equal its maximum degree.
Received November 10, 1998
RID="*"
ID="*" This work was carried out while the first author was visiting Nottingham, funded by Visiting Fellowship Research Grant
GR/L54585 from the Engineering and Physical Sciences Research Council. The work of this author was also partly supported by
grants 96-01-01614 and 97-01-01075 of the Russian Foundation for Fundamental Research. 相似文献
5.
6.
In 1995, Voigt constructed a planar triangle-free graph that is not 3-list-colorable. It has 166 vertices. Gutner then constructed such a graph with 164 vertices. We present two more graphs with these properties. The first graph has 97 vertices and a failing list assignment using triples from a set of six colors, while the second has 109 vertices and a failing list assignment using triples from a set of five colors. 相似文献
7.
A spanning subgraph H of a graph G is a 2-detour subgraph of G if for each x, y ∈ V(G), d
H
(x, y) ≤ d
G
(x, y) + 2. We prove a conjecture of Erdős, Hamburger, Pippert, and Weakley by showing that for some positive constant c and every n, each 2-detour subgraph of the n-dimensional hypercube Q
n
has at least clog2
n · 2
n
edges.
József Balogh: Research supported in part by NSF grants DMS-0302804, DMS-0603769 and DMS-0600303, UIUC Campus Reseach Board
#06139 and #07048, and OTKA 049398.
Alexandr Kostochka: Research supported in part by NSF grants DMS-0400498 and DMS-0650784, and grant 06-01-00694 of the Russian
Foundation for Basic Research. 相似文献
8.
O. V. Borodin A. O. Ivanova A. V. Kostochka 《Journal of Applied and Industrial Mathematics》2007,1(1):9-17
An oriented k-coloring of an oriented graph H is defined to be an oriented homomorphism of H into a k-vertex tournament. It is proved that every orientation of a graph with girth at least 5 and maximum average degree over all subgraphs less than 12/5 has an oriented 5-coloring. As a consequence, each orientation of a plane or projective plane graph with girth at least 12 has an oriented 5-coloring. 相似文献
9.
A. V. Kostochka 《Journal of Graph Theory》1995,19(1):65-67
The following is proved: if every bridgeless graph G has a cycle cover of length at most 7/5|E(G)|, then every bridgeless graph G has a cycle cover of length at most 7/5|E(G)| such that any edge of G is covered once or twice. © 1995 John Wiley & Sons, Inc. 相似文献
10.
Two graphs G1 and G2 of order n pack if there exist injective mappings of their vertex sets into [n], such that the images of the edge sets do not intersect. Sauer and Spencer proved that if Δ (G1) Δ (G2) < 0.5n, then G1 and G2 pack.
In this note, we study an Ore-type analogue of the Sauer–Spencer Theorem. Let θ(G) = max{d(u) + d(v): uv∈E(G)}. We show that if θ(G1)Δ(G2) < n, then G1 and G2 pack. We also characterize the pairs (G1,G2) of n-vertex graphs satisfying θ(G1)Δ(G2) = n that do not pack.
This work was supported in part by NSF grant DMS-0400498. The work of the first author was also partly supported by grant
05-01-00816 of the Russian Foundation for Basic Research. 相似文献