| บทคัดย่อ |
Let \(H = (V,E)\) be a hypergraph. The hypergraph \(H\) is said to be \(k - \)uniform if every edge \(e \in E,|e| = k\). A \(proper\) \(\lambda - \)\(coloring\) of \(H\) is a mapping \(c:V \to 1,2, \ldots ,\lambda \) for which every edge \(e \in E\) has at least two vertices of different colors. The minimum value of \(\lambda \) for which there exists a proper \(\lambda - \)\(coloring\) of a hypergraph \(H\) is called the \(chromatic\) \(number\) of \(H\), denoted by \(\chi (H)\). Let \(H{\rm{ }} = {\rm{ }}\left( {V,E} \right)\) be a hypergraph. The \(edge\) \(intersection\) \(graph\) \(L\left( H \right)\) of \(H\) is defined as
follows:
1. the vertices of \(L\left( H \right)\) are in a bijective correspondence with the edges of \(H\):
2. two vertices are adjacent in \(L\left( H \right)\) if and only of the corresponding edges have a nonempty intersection.
In this research, we give the chromatic number and the relation between \(k - \)uniform hypergraph and the chromatic number of its edge intersection graph.
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