On Weisfeiler-Leman Invariance: Subgraph Counts and Related Graph Properties

Autor:	Arvind, V., Fuhlbrück, Frank, Köbler, Johannes, Verbitsky, Oleg
Rok vydání:	2018
Předmět:	Computer Science - Discrete Mathematics Computer Science - Computational Complexity Computer Science - Logic in Computer Science
Druh dokumentu:	Working Paper
Popis:	The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a fruitful approach to the Graph Isomorphism problem. 2-WL corresponds to the original algorithm suggested by Weisfeiler and Leman over 50 years ago. 1-WL is the classical color refinement routine. Indistinguishability by $k$-WL is an equivalence relation on graphs that is of fundamental importance for isomorphism testing, descriptive complexity theory, and graph similarity testing which is also of some relevance in artificial intelligence. Focusing on dimensions $k=1,2$, we investigate subgraph patterns whose counts are $k$-WL invariant, and whose occurrence is $k$-WL invariant. We achieve a complete description of all such patterns for dimension $k=1$ and considerably extend the previous results known for $k=2$. Comment: The results on fractional graph parameters are excluded from this version and will appear as a separate paper
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1811.04801 Zobrazit plný text záznamu View this record from Arxiv