Every longest circuit of a 3‐connected,K3,3‐minor free graph has a chord
نویسندگان
چکیده
منابع مشابه
Every longest circuit of a 3-connected, K3, 3-minor free graph has a chord
Carsten Thomassen conjectured that every longest circuit in a 3-connected graph has a chord. We prove the conjecture for graphs having no K3,3 minor, and consequently for planar graphs. Carsten Thomassen made the following conjecture [1, 7]: Conjecture 1 (Thomassen) Every longest circuit of a 3-connected graph has a chord. That conjecture has been proved for planar graphs with minimum degree at...
متن کامل1 Every longest circuit of a 3-connected, K3,3-minor free graph has a chord
Carsten Thomassen conjectured that every longest circuit in a 3-connected graph has a chord. We prove the conjecture for graphs having no K3,3 minor, and consequently for planar graphs. Carsten Thomassen made the following conjecture [1, 7], where a circuit denotes a connected 2-regular graph: Conjecture 1 (Thomassen) Every longest circuit of a 3-connected graph has a chord. That conjecture has...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2008
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.20312