Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Fuhlbrück, Frank"'
We say that a vertex $v$ in a connected graph $G$ is decisive if the numbers of walks from $v$ of each length determine the graph $G$ rooted at $v$ up to isomorphism among all connected rooted graphs with the same number of vertices. On the other han
Externí odkaz:
http://arxiv.org/abs/2409.03690
We consider a hierarchy of graph invariants that naturally extends the spectral invariants defined by F\"urer (Lin. Alg. Appl. 2010) based on the angles formed by the set of standard basis vectors and their projections onto eigenspaces of the adjacen
Externí odkaz:
http://arxiv.org/abs/2310.04391
The $k$-dimensional Weisfeiler-Leman algorithm ($k$-WL) is a very useful combinatorial tool in graph isomorphism testing. We address the applicability of $k$-WL to recognition of graph properties. Let $G$ be an input graph with $n$ vertices. We show
Externí odkaz:
http://arxiv.org/abs/2005.08887
The $k$-dimensional Weisfeiler-Leman algorithm is a powerful tool in graph isomorphism testing. For an input graph $G$, the algorithm determines a canonical coloring of $s$-tuples of vertices of $G$ for each $s$ between 1 and $k$. We say that a numer
Externí odkaz:
http://arxiv.org/abs/2002.04590
The $k$-dimensional Weisfeiler-Leman procedure ($k$-WL), which colors $k$-tuples of vertices in rounds based on the neighborhood structure in the graph, has proven to be immensely fruitful in the algorithmic study of Graph Isomorphism. More generally
Externí odkaz:
http://arxiv.org/abs/1910.11325
As it is well known, the isomorphism problem for vertex-colored graphs with color multiplicity at most 3 is solvable by the classical 2-dimensional Weisfeiler-Leman algorithm (2-WL). On the other hand, the prominent Cai-F\"urer-Immerman construction
Externí odkaz:
http://arxiv.org/abs/1907.02892
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 ro
Externí odkaz:
http://arxiv.org/abs/1811.04801
Publikováno v:
In Information and Computation October 2022 288
Publikováno v:
In Theoretical Computer Science 4 December 2021 895:96-114
In this paper we study the complexity of the following problems: Given a colored graph X=(V,E,c), compute a minimum cardinality set S of vertices such that no nontrivial automorphism of X fixes all vertices in S. A closely related problem is computin
Externí odkaz:
http://arxiv.org/abs/1606.04383