Stability of graphs.
Stability of Kronecker products of irreducible characters of the symmetric group.
Stable equivalence over symmetric functions.
Stable graphs
Stable marriages. (Mariages stables.)
Stable properties of plethysm: on two conjectures of Foulkes.
Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.
It is not known whether or not the stable rational cohomology groups H*(Aut(F∞);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields...
Stable sets for -free graphs
The Maximum Stable Set (MS) problem is a well known NP-hard problem. However different graph classes for which MS can be efficiently solved have been detected and the augmenting graph technique seems to be a fruitful tool to this aim. In this paper we apply a recent characterization of minimal augmenting graphs [22] to prove that MS can be solved for -free graphs in polynomial time, extending some known results.
Stacks, queues and tracks: layouts of graph subdivisions.
Staircases in .
Standard character condition for table algebras.
Standard domino tableaux and asymptotic Hecke algebras
Standard monomials for q-uniform families and a conjecture of Babai and Frankl
Let n, k, α be integers, n, α>0, p be a prime and q=p α. Consider the complete q-uniform family We study certain inclusion matrices attached to F(k,q) over the field . We show that if l≤q−1 and 2l≤n then This extends a theorem of Frankl [7] obtained for the case α=1. In the proof we use arguments involving Gröbner bases, standard monomials and reduction. As an application, we solve a problem of Babai and Frankl related to the size of some L-intersecting families modulo q.
Standard paths in another composition poset.
Star coloring high girth planar graphs.
Star Coloring of Subcubic Graphs
A star coloring of an undirected graph G is a coloring of the vertices of G such that (i) no two adjacent vertices receive the same color, and (ii) no path on 4 vertices is bi-colored. The star chromatic number of G, χs(G), is the minimum number of colors needed to star color G. In this paper, we show that if a graph G is either non-regular subcubic or cubic with girth at least 6, then χs(G) ≤ 6, and the bound can be realized in linear time.
Star Complements and Maximal Exceptional Graphs
Star number and star arboricity of a complete multigraph
Let be a multigraph. The star number of is the minimum number of stars needed to decompose the edges of . The star arboricity of is the minimum number of star forests needed to decompose the edges of . As usual denote the -fold complete graph on vertices (i.e., the multigraph on vertices such that there are edges between every pair of vertices). In this paper, we prove that for
Star-Cycle Factors of Graphs
A spanning subgraph F of a graph G is called a star-cycle factor of G if each component of F is a star or cycle. Let G be a graph and f : V (G) → {1, 2, 3, . . .} be a function. Let W = {v ∈ V (G) : f(v) = 1}. Under this notation, it was proved by Berge and Las Vergnas that G has a star-cycle factor F with the property that (i) if a component D of F is a star with center v, then degF (v) ≤ f(v), and (ii) if a component D of F is a cycle, then V (D) ⊆ W if and only if iso(G − S) ≤ Σx∈S f(x) for all...
Starlike trees with maximum degree 4 are determined by their signless Laplacian spectra.