3-trees with Few Vertices of Degree 3 in Circuit Graphs
نویسندگان
چکیده
A circuit graph (G,C) is a 2-connected plane graph G with an outer cycle C such that from each inner vertex v, there are three disjoint paths to C . In this paper, we shall show that a circuit graph with n vertices has a 3-tree (i.e., a spanning tree with maximum degree at most 3) with at most n−7 3 vertices of degree 3. Our estimation for the number of vertices of degree 3 is sharp. Using this result, we prove that a 3-connected graph with n vertices on a surface Fχ with Euler characteristic χ ≥ 0 has a 3-tree with at most n 3 + cχ vertices of degree 3, where cχ is a constant depending only on Fχ . c © 2008 Elsevier B.V. All rights reserved.
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عنوان ژورنال:
- Discrete Mathematics
دوره 309 شماره
صفحات -
تاریخ انتشار 2009