Kneser graphsJohnson graphsDistance graphsExistence of designsLet G(n,r,s) be a graph whose vertices are all r-element subsets of an n-element set, in which two vertices are adjacent if they intersect in exactly s elements. In this paper we study chromatic numbers of G(n,r,s) with r...
Given integers k, n, 2 n0(k) the chromatic number of this graph is (k - 1)() + rs, where n = (k - 1)s + r, 0 ≤ r < k - 1.P. FranklCNRS 15 Quai A. France ParisJournal of Graph TheoryPeter Frankl. On the chromatic number of the general Kneser-graph. Journal of ...
Kneser graph Chromatic number Square of graph 1. Introduction For a finite set X, let Xk be the set of all k-element subsets of X. For n≥2k, for a finite set X with n elements, the Kneser graph K(n,k) is the graph whose vertex set is Xk and two vertices A and B are adjace...
Let ( G ) be the line-distinguishing chromatic number and x ( G ) the chromatic index of a graph G . We prove the relation ( G ) x ( G ), conjectured by Ha... NZ Salvi - John Wiley & Sons, Inc. 被引量: 7发表: 1993年 The Distinguishing Chromatic Number of Kneser Graphs A...
The total dominator chromatic number χtd(G) of G is the minimum number of color classes in a TDC of G. In this paper among some other results and by using the existence of Steiner triple systems, we determine the total dominator chromatic number of the Kneser graph KG(n,2) for each ...
The total dominator chromatic number χtd(G) of G is the minimum number of color classes in a TDC of G . In this paper among some other results and by using the existence of Steiner triple systems, we determine the total dominator chromatic number of the Kneser graph KG(n,2) for each...
In 1955 the number theorist Martin Kneser posed a seemingly innocuous problem that became one of the great challenges in graph theory until a brilliant and totally unexpected solution, using the "Borsuk–Ulam theorem" from topology, was found by László Lovász twenty-three years later....
In an earlier paper, the present authors (2015) introduced thealtermatic numberof graphs and used Tucker's lemma, an equivalent combinatorial version of the Borsuk-Ulam theorem, to prove that the altermatic number is a lower bound for chromatic number. A matching Kneser graph is a graph ...
chromatic numberq-analog of kneser graphWe show that the q-Kneser graph q K 2k:k (the graph on the K-subspaces of a 2K-space over GF(q), where two k-spaces are adjacent when they intersect trivially), has chromatic number q~k + q~(k-1) for k = 3 and for k < q log q -...
Kneser graphs﹕table Kneser graphs﹕table r〡rm Kneser hypergraphmultichromatic numberMycielskianp>For positive integers n and s , a subset [ n ] is s -stable if for distinct . The s -stable r -uniform Kneser hypergraph is the r -uniform hypergraph that has the collection of all s -...