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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 $(P ₆, K_{2, 3})$ -free graphs

Raffaele Mosca (2012)

Discussiones Mathematicae Graph Theory

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 $(P ₆, K_{2, 3})$ -free graphs in polynomial time, extending some known results.

Stacks, queues and tracks: layouts of graph subdivisions.

Dujmović, Vida, Wood, David R. (2005)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Staircases in $ℤ^{2}$ .

Breuer, Felix, von Heymann, Frederik (2010)

Integers

Standard character condition for table algebras.

Rahnamai Barghi, Amir, Bagherian, Javad (2010)

The Electronic Journal of Combinatorics [electronic only]

Standard domino tableaux and asymptotic Hecke algebras

William M. McGovern (1996)

Compositio Mathematica

Standard monomials for q-uniform families and a conjecture of Babai and Frankl

Gábor Hegedűs, Lajos Rónyai (2003)

Open Mathematics

Let n, k, α be integers, n, α>0, p be a prime and q=p α. Consider the complete q-uniform family $ℱ (k, q) = \{K \subseteq [n] : |K| \equiv k (m o d q)\}$ We study certain inclusion matrices attached to F(k,q) over the field $𝔽_{p}$ . We show that if l≤q−1 and 2l≤n then $r a n k_{𝔽_{p}} I (ℱ (k, q), (\begin{matrix} [n] \\ ⩽ ℓ \end{matrix})) ⩽ (\begin{matrix} n \\ ℓ \end{matrix})$ 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.

Snellman, Jan (2004)

The Electronic Journal of Combinatorics [electronic only]

Star coloring high girth planar graphs.

Timmons, Craig (2008)

The Electronic Journal of Combinatorics [electronic only]

Star Coloring of Subcubic Graphs

T. Karthick, C.R. Subramanian (2013)

Discussiones Mathematicae Graph Theory

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

P. Rowlinson (2004)

Publications de l'Institut Mathématique

Star number and star arboricity of a complete multigraph

Chiang Lin, Tay-Woei Shyu (2006)

Czechoslovak Mathematical Journal

Let $G$ be a multigraph. The star number $s (G)$ of $G$ is the minimum number of stars needed to decompose the edges of $G$ . The star arboricity $s a (G)$ of $G$ is the minimum number of star forests needed to decompose the edges of $G$ . As usual $λ K_{n}$ denote the $λ$ -fold complete graph on $n$ vertices (i.e., the multigraph on $n$ vertices such that there are $λ$ edges between every pair of vertices). In this paper, we prove that for $n \geq 2$ $...$

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