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{\bf He Chen and Xueliang Li}
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{\bf Color Neighborhood Union Conditions for Long Hetero\-chromatic Paths in Edge-Colored Graphs}
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Let $G$ be an edge-colored graph. A heterochromatic (rainbow, or
multicolored) path of $G$ is such a path in which no two edges have
the same color. Let $CN(v)$ denote the color neighborhood of a
vertex $v$ of $G$. In a previous paper, we showed that if
$|CN(u)\cup CN(v)|\geq s$ (color neighborhood union condition) for
every pair of vertices $u$ and $v$ of $G$, then $G$ has a
heterochromatic path of length at least
$\lfloor{2s+4\over5}\rfloor$. In the present paper, we prove that
$G$ has a heterochromatic path of length at least
$\lceil{s+1\over2}\rceil$, and give examples to show that the
lower bound is best possible in some sense.
\bye