Local planar dendritic structure: a uniquely biological phenomenon?
نویسندگان
چکیده
منابع مشابه
On uniquely partitionable planar graphs
Let ~1,22 . . . . . ~,; n/>2 be any properties of graphs. A vertex (~L, ~2 . . . . . J~,,)-partition of a graph G is a partition (V1, l~,...,/7,,) of V(G) such that for each i = 1,2 . . . . . n the induced subgraph G[Vi] has the property ~i. A graph G is said to be uniquely (~1,~2 . . . . . ~,)-partitionable if G has unique vertex (2~1, ~2 , . . . , ~,)-partition. In the present paper we invest...
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A k-chromatic graph G is called uniquely k-colorable if every k-coloring of the vertex set V of G induces the same partition of V into k color classes. There is an innnite class C of uniquely 4-colorable planar graphs obtained from the K 4 by repeatedly inserting new vertices of degree 3 in triangular faces. In this paper we are concerned with the well-known conjecture (see 6]) that every uniqu...
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We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (D1,D1)-partitionable planar graphs with respect to the property D1 ”to be a forest”.
متن کاملThe Size of Edge-critical Uniquely 3-Colorable Planar Graphs
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. A uniquely k-colorable graph G is edge-critical if G−e is not a uniquely k-colorable graph for any edge e ∈ E(G). In this paper, we prove that if G is an edge-critical uniquely 3-colorable planar graph, then |E(G)| 6 83 |V (G)| − 17 3 . On the other hand, there exis...
متن کاملSize of edge-critical uniquely 3-colorable planar graphs
A graph G is uniquely k-colorable if the chromatic number of G is k and G has only one k-coloring up to permutation of the colors. A uniquely k-colorable graph G is edge-critical if G − e is not a uniquely k-colorable graph for any edge e ∈ E(G). Mel’nikov and Steinberg [L. S. Mel’nikov, R. Steinberg, One counterexample for two conjectures on three coloring, Discrete Math. 20 (1977) 203-206] as...
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ژورنال
عنوان ژورنال: BMC Neuroscience
سال: 2009
ISSN: 1471-2202
DOI: 10.1186/1471-2202-10-s1-p4