## 15 Citations

Games on graphs, visibility representations, and graph colorings

- Mathematics
- 2016

In this thesis we study combinatorial games on graphs and some graph parameters whose consideration was inspired by an interest in the symmetry of hypercubes. A capacity function f on a graph G…

The Game Saturation Number of a Graph

- MathematicsJ. Graph Theory
- 2017

The lower bound on the length under optimal play of the P_4-saturation game on K_{m,n} is proved, which is similar to the results when Min plays first.

Domination Game: A proof of the 3/5-Conjecture for Graphs with Minimum Degree at Least Two

- MathematicsSIAM J. Discret. Math.
- 2016

It is proved that if $G$ is an $n$-vertex isolate-free graph with $\ell$ vertices of degree 1, then $\gamma_g(G) \le 3n/5 + \left \lceil \ell/2 \right \rceil + 1$; in the course of establishing this result, a question of Bresar e...

Paired-Domination Game Played in Graphs

- Mathematics
- 2019

In this paper, we continue the study of the domination game in graphs introduced by Bre{v{s}}ar, Klav{v{z}}ar, and Rall. We study the paired-domination version of the domination game which adds a…

Saturation Games for Odd Cycles

- MathematicsElectron. J. Comb.
- 2019

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.

Signless Laplacian spectral radius and matching in graphs

- Mathematics
- 2020

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…

## References

SHOWING 1-10 OF 29 REFERENCES

Tight Lower Bounds on the Size of a Maximum Matching in a Regular Graph

- MathematicsGraphs Comb.
- 2007

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)} .

A Problem in Graph Theory

- Mathematics
- 1964

A gruph consists of a finite set of vertices some pairs of which are adjacent, i.e., joined by an edge. No edge joins a vertex to itself and at most one edge joins any two vertices. The degree of a…

Connected, Bounded Degree, Triangle Avoidance Games

- MathematicsElectron. J. Comb.
- 2011

This work considers variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later, and determines the winner for all values of $n.

Bounded Degree, Triangle Avoidance Graph Games

- MathematicsGraphs Comb.
- 2013

This work considers variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal and determines the winner for all values of n.

Winning Fast in Sparse Graph Construction Games

- MathematicsCombinatorics, Probability and Computing
- 2008

If G is a d-degenerate graph on n vertices and N > d1122d+9n, then Maker can claim a copy of G in at most d1121d+7n rounds, and a lower bound on the number of rounds Maker needs to win is discussed.

Planarity, Colorability, and Minor Games

- MathematicsSIAM J. Discret. Math.
- 2008

The Maker-Breaker and Avoider-Enforcer versions of the planarity game, the $k$-colorability game, and the $K_t$-minor game are considered.

Fast Winning Strategies in Avoider-Enforcer Games

- EconomicsGraphs Comb.
- 2009

For several games that are known to be an Enforcer’s win, the minimum number of moves Enforcer has to play in order to win is estimated quite precisely.

On Hajnal's triangle-free game

- MathematicsGraphs Comb.
- 1992

This work investigates the triangle-free game proposed by András Hajnal and determines the winner in a version of the game with the additional rule that the chosen edges must always give a connected subgraph ofKn.

Subtrees and Subforests of Graphs

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. B
- 1994

The edge-number bound answers in the affirmative a conjecture due to Erdős and Sos and improved bounds for specified spanning subtrees of graphs are given.