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Characterizing graphs of maximum matching width at most 2. (English) Zbl 1395.05133
Summary: The maximum matching width is a width-parameter that is defined on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the graphs of maximum matching width at most $$2$$ using the minor obstruction set. Also, we compute the exact value of the maximum matching width of a grid.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C35 Extremal problems in graph theory
##### Keywords:
maximum matching width; minor obstructions; grid
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##### References:
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