منابع مشابه
RECURRENCE OF DISTRIBUTIONAL LIMITS OF FINITE PLANAR GRAPHS Itai Benjamini
Suppose that G j is a sequence of finite connected planar graphs, and in each G j a special vertex, called the root, is chosen randomly-uniformly. We introduce the notion of a distributional limit G of such graphs. Assume that the vertex degrees of the vertices in G j are bounded, and the bound does not depend on j. Then after passing to a subsequence, the limit exists, and is a random rooted g...
متن کاملRecurrence of Distributional Limits of Finite Planar Graphs
Suppose that Gj is a sequence of finite connected planar graphs, and in each Gj a special vertex, called the root, is chosen randomlyuniformly. We introduce the notion of a distributional limit G of such graphs. Assume that the vertex degrees of the vertices in Gj are bounded, and the bound does not depend on j. Then after passing to a subsequence, the limit exists, and is a random rooted graph...
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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 اولGraph recurrence
For a graph G, a graph recurrence sequence x0, x1, x2, . . . of vectors is defined by the recurrence xt+1 = Axt , t = 0, 1, . . . , where A is the adjacency matrix of G and x0 is an initial vector. Each vector in this sequence can be thought of as a vertex labeling of G, the label at a given vertex at step t +1 obtained by summing the values at the adjacent vertices at step t . Based on graphic...
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This paper concerns random bipartite planar maps which are defined by assigning weights to their faces. The paper presents a threefold contribution to the theory. Firstly, we prove the existence of the local limit for all choices of weights and describe it in terms of an infinite mobile. Secondly, we show that the local limit is in all cases almost surely recurrent. And thirdly, we show that fo...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2013
ISSN: 0003-486X
DOI: 10.4007/annals.2013.177.2.10