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- Center for Integrated Quantum Science and TechnologyDE58 papers
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6 papers · 2 filters
On some Graphs with a Unique Perfect Matching
S. Chaplick, M. Fürst, F. Maffray +1
We show that deciding whether a given graph of size has a unique perfect matching as well as finding that matching, if it exists, can be done in time if is eithe…
A lower bound on the acyclic matching number of subcubic graphs
M. Fürst, D. Rautenbach
The acyclic matching number of a graph is the largest size of an acyclic matching in , that is, a matching in such that the subgraph of induced by the vertices i…
On some hard and some tractable cases of the maximum acyclic matching problem
M. Fürst, D. Rautenbach
Three well-studied types of subgraph-restricted matchings are induced matchings, uniquely restricted matchings, and acyclic matchings. While it is hard to determine the maximum siz…
On the Kőnig-Egerváry Theorem for -Paths
Stéphane Bessy, Pascal Ochem, Dieter Rautenbach
The famous Kőnig-Egerváry theorem is equivalent to the statement that the matching number equals the vertex cover number for every induced subgraph of some graph if and only if tha…
Locally Searching for Large Induced Matchings
Maximilian Fürst, Marilena Leichter, Dieter Rautenbach
It is an easy observation that a natural greedy approach yields a -factor approximation algorithm for the maximum induced matching problem in -regular graph…
Degenerate Matchings and Edge Colorings
Julien Baste, Dieter Rautenbach
A matching in a graph is -degenerate if the subgraph of induced by the set of vertices incident with an edge in is -degenerate. Goddard, Hedetniemi, Hedetniem…