منابع مشابه
Asymmetric directed graph coloring games
This note generalizes the (a, b)-coloring game and the (a, b)-marking game which were introduced by Kierstead [7] for undirected graphs to directed graphs. We prove that the (a, b)-chromatic and (a, b)-coloring number for the class of orientations of forests is b + 2 if b ≤ a, and infinity otherwise. From these results we deduce upper bounds for the (a, b)-coloring number of oriented outerplana...
متن کاملAsymmetric graph coloring games
We introduce the (a; b)-coloring game, an asymmetric version of the coloring game played by two players Alice and Bob on a finite graph, which differs from the standard version in that, in each turn, Alice colors a vertices and Bob colors b vertices. We also introduce a related game, the (a; b)-marking game. We analyze these games and determine the (a; b)chromatic numbers and (a;b)-coloring num...
متن کاملAsymmetric Coloring Games on Incomparability Graphs
Consider the following game on a graph G: Alice and Bob take turns coloring the vertices of G properly from a fixed set of colors; Alice wins when the entire graph has been colored, while Bob wins when some uncolored vertices have been left. The game chromatic number of G is the minimum number of colors that allows Alice to win the game. The game Grundy number of G is defined similarly except t...
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در این پایان نامه رنگ آمیزی دینامیکی یک گراف را بیان و مطالعه می کنیم. یک –kرنگ آمیزی سره ی رأسی گراف g را رنگ آمیزی دینامیکی می نامند اگر در همسایه های هر رأس v?v(g) با درجه ی حداقل 2، حداقل 2 رنگ متفاوت ظاهر شوند. کوچکترین عدد صحیح k، به طوری که g دارای –kرنگ آمیزی دینامیکی باشد را عدد رنگی دینامیکی g می نامند و آنرا با نماد ?_2 (g) نمایش می دهند. مونت گمری حدس زده است که تمام گراف های منتظم ...
15 صفحه اولThe Shapley value for directed graph games
The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is defined as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. We assume that in order to cooperate players may join only ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.03.022