\input zb-basic
\input zb-ioport
\iteman{io-port 06190263}
\itemau{Martinh\~ao, A.N.; Monte Carmelo, E.L.}
\itemti{Short coverings and matching in weighted graphs.}
\itemso{Bonomo, Flavia (ed.) et al., LAGOS'11 -- VI Latin-American algorithms, graphs, and optimization symposium. Extended abstracts from the symposium, Bariloche, Argentina, March 28--April 1, 2011. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 37, 321-326 (2011).}
\itemab
Summary: Given a prime power $q$, the number $c(q)$ denotes the minimum cardinality of a subset $\mathcal{H}$ of $\mathbb{F}_{q}^{3}$ which satisfies the following property: every element in this space differs in at most 1 coordinate from a scalar multiple of a vector in $\mathcal{H}$. In this work, the upper bound on $c(q)$ is improved when $q$ is odd. The method is based on $\omega$-partition, a combinatorial concept which can be also reformulated as a kind of matching in weighted graph.
\itemrv{~}
\itemcc{}
\itemut{covering; finite field; $\omega$-partition; weighted graph; matching}
\itemli{doi:10.1016/j.endm.2011.05.055}
\end