
Linear Programming complementation and its application to fractional graph theory
In this paper, we introduce a new kind of duality for Linear Programming...
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Fractional Covers of Hypergraphs with Bounded MultiIntersection
Fractional (hyper)graph theory is concerned with the specific problems ...
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Fractional matchings and componentfactors of (edgechromatic critical) graphs
The paper studies componentfactors of graphs which can be characterized...
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Fractional homomorphism, WeisfeilerLeman invariance, and the SheraliAdams hierarchy for the Constraint Satisfaction Problem
Given a pair of graphs A and B, the problems of deciding whether there e...
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Information theoretic parameters of noncommutative graphs and convex corners
We establish a second antiblocker theorem for noncommutative convex co...
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On the WeisfeilerLeman Dimension of Fractional Packing
The kdimensional WeisfeilerLeman procedure (kWL), which colors ktupl...
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Equitable Partitions into Matchings and Coverings in Mixed Graphs
Matchings and coverings are central topics in graph theory. The close re...
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Fractional hypergraph isomorphism and fractional invariants
Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like connectivity, clique and independence numbers, chromatic number, vertex and edge cover numbers, matching number, domination and total domination numbers. In this work, we extend the concept of fractional graph isomorphism to hypergraphs, and give an alternative characterization, analogous to one of those that are known for graphs. With this new concept we prove that the fractional packing, covering, matching and transversal numbers on hypergraphs are invariant under fractional hypergraph isomorphism. As a consequence, fractional matching, vertex and edge cover, independence, domination and total domination numbers are invariant under fractional graph isomorphism. This is not the case of fractional chromatic, clique, and clique cover numbers. In this way, most of the classical fractional parameters are classified with respect to their invariance under fractional graph isomorphism.
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