Extremal combinatorics in generalized Kneser graphs - Mussche - 2009 () Citation Context ...f qKn:k are adjacent if and only if the corresponding k-subspaces are disjoint. In [3], the chromatic number of the q-Kneser graph qKn:2 is determined, and the minimum colorings are characterized...
For example, the Kneser graphs are known to have odd girth 2⌈kv−2k⌉+1, as proved in [6], which meets the bound given in [4, p. 146], and which simplifies to 2k+1 in the case of the Odd graphs. The Johnson graphs are distance-regular (see [2] or [4]) but not tria...
Hamilton paths Generalized Petersen graph 1. Introduction For positive integers n and k, with n≥3, the generalized Petersen graph P(n,k) is the graph obtained from an n-cycle (u0,u1,…,un−1,un) by adding a pendant edge uivi at each ui and then joining vi and vj if |j−i|...
Generalized Kneser graphsJohnson graphsThreshold graphsClique complexIn chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy?
The generalized Johnson graph G (n , k , t) is the graph whose vertices are the k -subsets of the set { 1 , 2 , ... , n } , and two vertices are adjacent if and only if they intersect with t elements. Special cases of generalized Johnson graph include the Kneser graph G (n...
Only in 2000, Matouek provided the first combinatorial proof of the Kneser conjecture. Here we provide a hypergraph coloring theorem, with a combinatorial proof, which has as special cases the Kneser conjecture as well as its extensions and generalization by (hyper)graph coloring theorems of Dol'...
Johnson graphKneser graphlarge cyclesrandom walkCHROMATIC NUMBERSMALL SUBGRAPHSKNESERDIAMETERCODESGIRTHWe count cycles of an unbounded length in generalized Johnson graphs. Asymptotics of the number of such cycles is obtained for certain growth rates of the cycle length....
The generalized Kneser graph K ( n , r , s ) is the graph whose vertex-set is [ n ] r where two r-subsets A and B are joined by an edge if | A ∩ B | s. This note determines the diameter of generalized Kneser graphs. More precisely, the diameter of K ( n , r , s )...
Kneser graphsHadamard MatricesChromatic numberLet n>k>d be positive integers. The generalized Kneser graph K(n,k,d) is a graph whose vertices are all the subsets of size k in {1,…,n} and two subsets are adjacent if and only if they have less than d elements in common. For d=1 ...
We determine the chromatic number of some graphs of flags in buildings of type A 4 , namely of the Kneser graphs of flags of type { 2 , 4 } in the vector spaces G F ( q ) 5 for q ≥ 3 , and of the Kneser graph of flags of type { 2 , 3 } in the vector spaces G F ...