A planarity criterion for cubic bipartite graphs
نویسندگان
چکیده
We prove that a simple finite bipartite cubic non-planar graph contains a clean subdivision of K3.3. Here a subdivision of K3,3 is defined 1o be clean if it can be obtained from K3,3 by subdividing any edge by an even number of vertices. The proof is constructive and gives rise to a polynomial-time algorithm. @ 1998 Elsevier Science B.V. All rights reserved
منابع مشابه
The quantum sl(3) invariants of cubic bipartite planar graphs
Temperley-Lieb algebras have been generalized to sl(3, C) web spaces. Since a cubic bipartite planar graph with suitable directions on edges is a web, the quantum sl(3) invariants naturally extend to all cubic bipartite planar graphs. First we completely classify them as a connected sum of primes webs. We also provide a method to find all prime webs and exhibit all prime webs up to 20 vertices....
متن کاملOn Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges
A tree containing exactly two non-pendant vertices is called a double-star. Let $k_1$ and $k_2$ be two positive integers. The double-star with degree sequence $(k_1+1, k_2+1, 1, ldots, 1)$ is denoted by $S_{k_1, k_2}$. It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching. In this paper, we study the $S_{1,2}$-decomposit...
متن کاملBeyond-Planarity: Density Results for Bipartite Graphs
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly-planar. Here, planarity is relaxed by allowing edge crossings, but only with respect to some local forbidden crossing configurations. Early research dates back to the 1960s (e.g., Avital and Hanani [14]) for extremal problems on geometric graphs, but is also related to graph drawing problems ...
متن کاملThe projective plane crossing number of the circulant graph C(3k;{1, k})
The crossing number is an important measure of the non-planarity of a graph. Bhatt and Leighton [1] showed that the crossing number of a network (graph) is closely related to the minimum layout area required for the implementation of a VLSI circuit for that network. In general, determining the crossing number of a graph is hard. Garey and Johnson [3] showed that it is NP-complete. In fact, Hlin...
متن کاملEmbedding graphs in surfaces: MacLane’s theorem for higher genus∗
Given a closed surface S, we characterise the graphs embeddable in S by an algebraic condition asserting the existence of a sparse generating set for their cycle space. When S is the sphere, the condition defaults to MacLane’s planarity criterion.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 191 شماره
صفحات -
تاریخ انتشار 1998