Game matching number of graphs

@article{Cranston2013GameMN,
  title={Game matching number of graphs},
  author={Daniel W. Cranston and Bill Kinnersley and O Suil and Douglas B. West},
  journal={Discret. Appl. Math.},
  year={2013},
  volume={161},
  pages={1828-1836}
}
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Saturation Games for Odd Cycles
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It is shown that the number of edges that are in the final graph when both players play optimally is the same, andsat_g(\mathcal{C}_\infty\setminus C_3;n) is proved to be 2n-2, where $k\ge 2$ denotes the set of all odd cycles.
The generalized matcher game
Signless Laplacian spectral radius and matching in graphs
The signless Laplacian matrix of a graph $G$ is given by $Q(G)=D(G)+A(G)$, where $D(G)$ is a diagonal matrix of vertex degrees and $A(G)$ is the adjacency matrix. The largest eigenvalue of $Q(G)$ is
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Tight lower bounds on the size of a maximum matching in a regular graph of order n and α′(G) are studied, which show that if k is even, then α' (G) \ge \min \left(k^3-k^2-2) \, n - 2k + 2}{2(k-3-3k)} .
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