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- W2090817462 abstract "Let $G$ be a finite directed graph, $beta(G)$ the minimum size of a subset $X$ of edges such that the graph $G' = (V,E smallsetminus X)$ is directed acyclic and $gamma(G)$ the number of pairs of nonadjacent vertices in the undirected graph obtained from $G$ by replacing each directed edge with an undirected edge. Chudnovsky, Seymour and Sullivan cite{CSS07} proved that if $G$ is triangle-free, then $beta(G) leq gamma(G)$. They conjectured a sharper bound (so called the conjecture) that $beta(G) leq dfrac{gamma(G)}{2}$. Nathanson and Sullivan verified this conjecture for the directed Cayley graph $Cay(bbZ/NbbZ, E_A)$ whose vertex set is the additive group $bbZ/NbbZ$ and whose edge set $E_A$ is determined by $E_A = {(x,x+a) : x in bbZ/NbbZ, a in A}$ when $N$ is prime in cite{NS07} by introducing height. In this work, we extend the definition of height and the proof of CSS conjecture for $Cay(bbZ/NbbZ, E_A)$ to any positive integer $N$." @default.
- W2090817462 created "2016-06-24" @default.
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- W2090817462 date "2008-05-03" @default.
- W2090817462 modified "2023-10-15" @default.
- W2090817462 title "Nathanson's Heights and the CSS Conjecture for Cayley Graphs" @default.
- W2090817462 hasPublicationYear "2008" @default.
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