منابع مشابه
Game matching number of graphs
We study a competitive optimization version of α(G), the maximum size of a matching in a graph G. Players alternate adding edges of G to a matching until it becomes a maximal matching. One player (Max) wants that matching to be large; the other (Min) wants it to be small. The resulting sizes under optimal play when Max or Min starts are denoted α g(G) and α̂ ′ g(G), respectively. We show that al...
متن کاملGame chromatic number of graphs
y Abstract We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particular, since a planar graph has acyclic chromatic number at most 5, we conclude that the g...
متن کاملThe augmented Zagreb index, vertex connectivity and matching number of graphs
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
متن کاملCircular game chromatic number of graphs
In a circular r-colouring game on G, Alice and Bob take turns colour the vertices of G with colours from the circle S(r) of perimeter r. Colours assigned to adjacent vertices need to have distance at least 1 in S(r). Alice wins the game if all vertices are coloured, and Bob wins the game if some uncoloured vertices have no legal colour. The circular game chromatic number χcg(G) of G is the infi...
متن کاملThe game chromatic number of graphs
Suppose G = (V, E) is a graph. The game chromatic number of G is defined through a two-person game: the colouring game. Given a graph G and a set C of colours, Alice and Bob, with Alice playing first, take turns in playing the game. Each play by either player consists of colouring an uncoloured vertex of G with a colour from C. Both players need to respect the rule that no adjacent vertices sho...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.03.010