Counting the number of perfect matchings in graphs is a computationally hard problem. However, in the case of planar graphs, and even for K3,3-free graphs, the number of perfect matchings can be computed efficiently. The technique to achieve this is to ...
The anti-Ramsey number A R ( G , H ) is the maximum number of colors in an edge-coloring of a graph in the family G without any rainbow copy of H. The anti-Ramsey number for matchings has been studied extensively in several graph families, while ...
A graph is total domination edge-critical if the addition of any edge decreases the total domination number, while a graph with minimum degree at least two is total domination vertex-critical if the removal of any vertex decreases the total domination ...
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