Abstract
The Maximum clique problem (MCP) is graph theory problem that demand complete subgraf with maximum cardinality (maximum clique) in arbitrary graph. Solving MCP usually use Branch and Bound (BnB) algorithm, in this paper we will show how n + 1 color classes (where n is the difference between upper and lower bound) selected to form k-clique covering vertex set which later used for branching strategy can guarenteed finnding maximum clique.
Highlights
IntroductionThe method for determining the k-clique covering vertex set uses a color class, but they note that this method can guarantee that the set has a minimum size so that it will affect the length of the branching process, we realize that choosing an incorrect color class can causing no maximum clique to be found
The maximum clique problem (MCP) is the problem of finding a complete subgraph with the maximum number of vertices in it on any graph G = (V, E), the maximum clique cardinality in G is denoted by ω(G)
Pardalos and Xue (1994) formulated three main keys to the Branch and Bound (BnB) algorithm for MCP, namely: (1) How is a good lower bound? (2) How is a good upper bound of the maximum clique size determined? (3) How is the search carried out?
Summary
The method for determining the k-clique covering vertex set uses a color class, but they note that this method can guarantee that the set has a minimum size so that it will affect the length of the branching process, we realize that choosing an incorrect color class can causing no maximum clique to be found.
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