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2-reachable subsets in two-colored graphs

arxiv.org · 168 words · saved by 1 readers

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2-reachable subsets in two-colored graphs A subset $X$ of vertices in a graph $G$ is a {\em diameter 2 subset} if the distance of any two vertices of $X$ is at most two {\em in $G[X]$}. Relaxing this notion, a subset $X$ of vertices in a graph $G$ is a {\em 2-reachable subset} if the distance of any two vertices of $X$ is at most two {\em in $G$}. Related to recent attempts to strengthen a well-known conjecture of Ryser, English et al. conjectured that the vertices of a $2$-edge-colored cocktail party graph (the graph obtained from a complete graph with an even number of vertices by deleting

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