Independent paths and K5-subdivisions
نویسندگان
چکیده
A well known theorem of Kuratowski states that a graph is planar iff it contains no subdivision of K5 or K3,3. Seymour conjectured in 1977 that every 5-connected nonplanar graph contains a subdivision of K5. In this paper, we prove several results about independent paths (no vertex of a path is internal to another), which are then used to prove Seymour’s conjecture for two classes of graphs. These results will be used in a subsequent paper to prove Seymour’s conjecture for graphs containing K− 4 , which is a step in a program to approach Seymour’s conjecture. AMS Subject Classification: 05C38, 05C40, 05C75
منابع مشابه
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 100 شماره
صفحات -
تاریخ انتشار 2010