Coloring graphs with locally few colors
Discrete Mathematics
A Sperner-type theorem and qualitative independence
Journal of Combinatorial Theory Series A
Qualitative independence and Sperner problems for directed graphs
Journal of Combinatorial Theory Series A
On the Sperner Capacity of the Cyclic Triangle
Journal of Algebraic Combinatorics: An International Journal
The Sperner Capacity of Linear and Nonlinear Codes for the Cyclic Triangle
Journal of Algebraic Combinatorics: An International Journal
Capacities: from information theory to extremal set theory
Journal of Combinatorial Theory Series A
European Journal of Combinatorics
Orientations of self-complementary graphs and the relation of Sperner and Shannon capacities
European Journal of Combinatorics
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
IEEE Transactions on Information Theory
A nontrivial lower bound on the Shannon capacities of the complements of odd cycles
IEEE Transactions on Information Theory
Permutation Capacities of Families of Oriented Infinite Paths
SIAM Journal on Discrete Mathematics
Vertex cover in graphs with locally few colors
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Vertex cover in graphs with locally few colors
Information and Computation
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We introduce a directed analog of the local chromatic number defined by Erdös et al. [Discrete Math. 59 (1986) 21-34] and show that it provides an upper bound for the Sperner capacity of a directed graph. Applications and variants of this result are presented. In particular, we find a special orientation of an odd cycle and show that it achieves the maximum of Sperner capacity among the differently oriented versions of the cycle. We show that apart from this orientation, for all the others an odd cycle has the same Sperner capacity as a single edge graph. We also show that the (undirected) local chromatic number is bounded from below by the fractional chromatic number while for power graphs the two invariants have the same exponential asymptotics (under the co-normal product on which the definition of Sperner capacity is based). We strengthen our bound on Sperner capacity by introducing a fractional relaxation of our directed variant of the local chromatic number.