
TL;DR
This paper introduces 'Local Separators' in graphs to extend sparse graph theory to large networks, providing new decomposition theorems and characterizations relevant for analyzing complex graph structures.
Contribution
It presents the concept of local 2-separators, a decomposition theorem similar to the 2-separator theorem, and characterizes graphs without bounded wheel subdivisions.
Findings
Decomposition theorem for graphs using local 2-separators
Characterization of graphs with no bounded wheel subdivision
Extension of sparse graph theory to large networks
Abstract
How can sparse graph theory be extended to large networks, where algorithms whose running time is estimated using the number of vertices are not good enough? I address this question by introducing 'Local Separators' of graphs. Applications include: 1. A unique decomposition theorem for graphs along their local 2-separators analogous to the 2-separator theorem; 2. an exact characterisation of graphs with no bounded subdivision of a wheel.
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph theory and applications
