On Kneser Extensions
نویسندگان
چکیده
منابع مشابه
On Generalised Kneser Colourings
There are two possible definitions of the “s-disjoint r-uniform Kneser hypergraph” of a set system T : The hyperedges are either r-sets or r-multisets. We point out that Ziegler’s (combinatorial) lower bound on the chromatic number of an s-disjoint r-uniform Kneser hypergraph only holds if we consider r-multisets as hyperedges. We give a new proof of his result and show by example that a simila...
متن کاملOn generalized Kneser hypergraph colorings
In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs KG sS, “generalized r-uniform Kneser hypergraphs with intersection multiplicities s.” It generalized previous lower bounds by Kř́ıž (1992/2000) for the case s = (1, . . . , 1) without intersection multiplicities, and by Sarkaria (1990) for S = ([n] k ) . Here we discuss subtleties and difficulti...
متن کاملVariations on the Tait-Kneser theorem
At every point, a smooth plane curve can be approximated, to second order, by a circle; this circle is called osculating. One may think of the osculating circle as passing through three infinitesimally close points of the curve. A vertex of the curve is a point at which the osculating circle hyper-osculates: it approximates the curve to third order. Equivalently, a vertex is a critical point of...
متن کاملOn b-coloring of the Kneser graphs
A b-coloring of a graph G by k colors is a proper k-coloring of G such that in each color class there exists a vertex having neighbors in all the other k− 1 color classes. The b-chromatic number of a graph G, denoted by φ(G), is the maximum k for which G has a b-coloring by k colors. It is obvious that χ(G) ≤ φ(G). A graph G is b-continuous if for every k between χ(G) and φ(G) there is a b-colo...
متن کاملOn Fall Colorings of Kneser Graphs
A fall k-coloring of a graph G is a proper k-coloring of G such that each vertex of G sees all k colors on its closed neighborhood. In this note, we characterize all fall colorings of Kneser graphs of type KG(n, 2) for n ≥ 2 and study some fall colorings of KG(n,m) in some special cases and introduce some bounds for fall colorings of Kneser graphs.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.7308