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We give a new proof that any candy-passing game on a graph G with at least 4|E(G)|-|V(G)| candies stabilizes. (This result was first proven in arXiv:0807.4450.) Unlike the prior literature on candy-passing games, we use methods from the general theory of chip-firing games which allow us to obtain a polynomial bound on the number of rounds before stabilization.
Maker-Breaker games are played on a hypergraph $(X,mathcal{F})$, where $mathcal{F} subseteq 2^X$ denotes the family of winning sets. Both players alternately claim a predefined amount of edges (called bias) from the board $X$, and Maker wins the game
Switches are operations which make local changes to the edges of a graph, usually with the aim of preserving the vertex degrees. We study a restricted set of switches, called triangle switches. Each triangle switch creates or deletes at least one tri
We study analogues of $mathcal{F}$-saturation games, first introduced by Furedi, Reimer and Seress in 1991, and named as such by West. We examine analogous games on directed graphs, and show tight results on the walk-avoiding game. We also examine an
An extension of the well-known Szeged index was introduced recently, named as weighted Szeged index ($textrm{sz}(G)$). This paper is devoted to characterizing the extremal trees and graphs of this new topological invariant. In particular, we proved t
An edge-coloring of a graph $G$ with colors $1,ldots,t$ is an emph{interval $t$-coloring} if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an integer interval. It is well-known that there are graphs