The smallest hard-to-color graph for the SL algorithm
نویسندگان
چکیده
For a given approximate vertex coloring algorithm a graph is said to be slightly hard-tocolor (SHC) if some implementation of the algorithm uses more colors than the minimum needed. Similarly, a graph is said to be hard-to-color (HC) if every implementation of the algorithm results in a nonoptimal coloring. We study smallest such graphs for the smallest-last (SL) coloring algorithm. Our main result is that the prism is a unique smallest SHC graph and the prismatoid is a unique smallest HC graph for the SL algorithm.
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الگوریتم ژنتیک با جهش آشوبی هوشمند و ترکیب چند‌نقطه‌ای مکاشفه‌ای برای حل مسئله رنگ‌آمیزی گراف
Graph coloring is a way of coloring the vertices of a graph such that no two adjacent vertices have the same color. Graph coloring problem (GCP) is about finding the smallest number of colors needed to color a given graph. The smallest number of colors needed to color a graph G, is called its chromatic number. GCP is a well-known NP-hard problems and, therefore, heuristic algorithms are usually...
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عنوان ژورنال:
- Discrete Mathematics
دوره 164 شماره
صفحات -
تاریخ انتشار 1997