منابع مشابه
Partitioning a triangle-free planar graph into a forest and a forest of bounded degree
An (F , Fd)-partition of a graph is a vertex-partition into two sets F and Fd such that the graph induced by F is a forest and the one induced by Fd is a forest with maximum degree at most d. We prove that every triangle-free planar graph admits an (F , F5)-partition. Moreover we show that if for some integer d there exists a trianglefree planar graph that does not admit an (F , Fd)-partition, ...
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We give a new example of a triangle-free cc-chromatic graph: the vertices of G form a oox oo matrix, V(G) = [vi,i], i, j = 1, 2, ... The vertex vi,i is connected with every vertex of the ( i + j)th column. G is triangle-free: if A has the smallest column-index among {A, B, C}c V(G) and AB, ACEE(G), then B, Care in the same column so BC¢E(G). G is infinite-chromatic: ~ ~ {1, 2, ... } denotes the...
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Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and D ≥ 3. Assume the intersection numbers a1 = 0 and a2 6= 0. We show Γ is 3-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229].
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In this paper we investigate edge partition problems of the countable triangle free homogeneous graph. As consequences of the main result, we obtain the following theorems. For every coloring of the edges of the countable triangle free homogeneous graph 0//with finitely many colors there exists a copy of q/in q/whose edges are colored with at most two of the colors. The countable triangle free ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2014.08.010