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Les moments microlocaux et la régularité des solutions de l'équation de Schrödinger

Séminaire Équations aux dérivées partielles (Polytechnique)

Gain of regularity for equations of KdV type

Annales de l'I.H.P. Analyse non linéaire

The set chromatic number of a graph

Discussiones Mathematicae Graph Theory

For a nontrivial connected graph G, let c: V(G)→ N be a vertex coloring of G where adjacent vertices may be colored the same. For a vertex v of G, the neighborhood color set NC(v) is the set of colors of the neighbors of v. The coloring c is called a set coloring if NC(u) ≠ NC(v) for every pair u,v of adjacent vertices of G. The minimum number of colors required of such a coloring is called the set chromatic number χₛ(G) of G. The set chromatic numbers of some well-known classes of graphs are determined...

Set vertex colorings and joins of graphs

Czechoslovak Mathematical Journal

For a nontrivial connected graph $G$, let $c\phantom{\rule{0.222222em}{0ex}}V\left(G\right)\to ℕ$ be a vertex coloring of $G$ where adjacent vertices may be colored the same. For a vertex $v$ of $G$, the neighborhood color set $\mathrm{NC}\left(v\right)$ is the set of colors of the neighbors of $v$. The coloring $c$ is called a set coloring if $\mathrm{NC}\left(u\right)\ne \mathrm{NC}\left(v\right)$ for every pair $u,v$ of adjacent vertices of $G$. The minimum number of colors required of such a coloring is called the set chromatic number ${\chi }_{s}\left(G\right)$. A study is made of the set chromatic number of the join $G+H$ of two graphs $G$ and $H$. Sharp lower and upper bounds...

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