Modular intersection graphs
type: Item
instance of: scholarly article
title: Modular intersection graphs
zbMATH Open document ID: 0858.05091
DOI: 10.1007/BF01858460
author: Chi Wang
author: F. R. McMorris
published in: Graphs and Combinatorics
publication date: 1996-10-13T00:00:00Z
review text: A graph \(G=(V,E)\) is a modular intersection graph on a finite set \(U\) if there is a family of subsets \(S=\{S_x\mid x\in V\}\) of \(U\) and positive integers \(t<m\) such that \(\{x,y\}\) is an edge of \(G\) if and only if there is an integer \(r\) with \(t\leq r<m\) such that \(|S_x\cap S_y|\equiv r\pmod m\). The special cases considered include modular interval graphs (\(U\) is the vertex set of a path and each \(S_x\) is connected), modular subtree graphs (\(U\) is the vertex set of a tree and each \(S_x\) is connected), and parity intersection graphs (\(t=1\) and \(m=2\)).
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 934039
zbMATH Keywords: intersection graph
zbMATH Keywords: interval graphs
zbMATH Keywords: subtree graphs
MaRDI profile type: Publication
cites work: A decomposition theorem for partially ordered sets
cites work: The intersection graphs of subtrees in trees are exactly the chordal graphs
cites work: Q3663338
cites work: Q4873748
cites work: Intersection graphs of paths in a tree
cites work: Q4138414
full work available at URL: https://doi.org/10.1007/bf01858460
OpenAlex ID: W2061421770
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description: scientific article; zbMATH DE number 934039