Discussion on Maximal Edge-ideal in Graph Theory
Takaaki Fujita
*
Independent Research, Shinjuku, Shinjuku-ku, Tokyo, Japan.
*Author to whom correspondence should be addressed.
Abstract
The exploration of width parameters within the fields of graph theory and algebra has garnered significant interest. Among these parameters, tree-cut decomposition stands out as a vital metric. The "Edge-Tangle" concept is intrinsically linked to the width parameter known as "tree-cut width" in graph theory. In this paper, we introduce a new definition termed Maximal Edge-Ideal for graphs and demonstrate their equivalence to Edge-Tangles.
Keywords: Ideal, tangle, edge-tangle, tree-cut-width, tree-cut-decomposition