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Let $v(n)$ be the minimum number of voters with transitive preferences which are needed to generate any strong preference pattern (ties not allowed) on $n$ candidates. Let $k=\lfloor \log_2 n\rfloor$....
Note on group distance magic graphs $G[C_4]$
distance magic labeling magic constant sigma labeling graph labeling Abelian group
2012/4/23
A \emph{group distance magic labeling} or a $\gr$-distance magic labeling of a graph $G(V,E)$ with $|V | = n$ is an injection $f$ from $V$ to an Abelian group $\gr$ of order $n$ such that the weight $...
A note on the minimum skew rank of powers of paths
minimum skew rank path (strict) power of a graph Combinatorics
2011/9/5
Abstract: The real minimum skew rank of a simple graph G is the smallest possible rank among all real skew symmetric matrices, whose (i,j)-entry (for i not equal to j) is nonzero whenever {i, j} is an...
Abstract: We prove a general lemma about partitioning the vertex set of a graph into subgraphs of bounded degree. This lemma extends a sequence of results of Lov\'asz, Catlin, Kostochka and Rabern.
A note on a matrix version of the Farkas lemma
Farkas Lemma matrix polynomials Positivstellensatz
2011/2/28
A linear polyomial non-negative on the non-negativity domain of finitely many linear polynomials can be expressed as their non-negative linear combination. Recently, under several additional assumptio...