The structure of 1-planar graphs
نویسندگان
چکیده
A graph is called 1-planar if it can be drawn in the plane so that each its edge is crossed by at most one other edge. In the paper, we study the existence of subgraphs of bounded degrees in 1-planar graphs. It is shown that each 1-planar graph contains a vertex of degree at most 7; we also prove that each 3-connected 1-planar graph contains an edge with both endvertices of degrees at most 20, and we present similar results concerning bigger structures in 1-planar graphs with additional constraints. © 2006 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 307 شماره
صفحات -
تاریخ انتشار 2007