Proof of the strong 2-Cover Conjecture for planar graphs
نویسندگان
چکیده
منابع مشابه
Proof of Berge's strong path partition conjecture for k=2
Berge’s strong path partition conjecture from 1982 generalizes and extends Dilworth’s theorem and the Greene–Kleitman theorem which are well known for partially ordered sets. The conjecture is known to be true for all digraphs only for k = 1 (by the Gallai–Milgram theorem) and for k ≥ λ (where λ is the cardinality of the longest path in the graph). The attempts made, so far, to prove the conjec...
متن کامل20 Years of Negami's Planar Cover Conjecture
In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoods bijectively) if and only if G embeds in the projective plane. Though the ”if” direction is easy, and over ten related research papers have been published during the past 20 years of investigation, this beautiful con...
متن کاملProof of the oval conjecture for proper planar partition surfaces
We prove the ‘oval conjecture’ for planar partition functions, which says that the shift plane and the translation plane defined by a planar partition function form an oval pair of planes in the sense that each non-vertical line of one plane defines a topological oval in the projective closure of the other. The proof uses covering space techniques, and we have to assume that the generating func...
متن کاملOn the cover time of planar graphs
The cover time of a finite connected graph is the expected number of steps needed for a simple random walk on the graph to visit all the vertices. It is known that the cover time on any n-vertex, connected graph is at least (
متن کاملErdös-Gyárfás Conjecture for Cubic Planar Graphs
In 1995, Paul Erdős and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer m such that G contains a simple cycle of length 2m. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1986
ISSN: 0095-8956
DOI: 10.1016/0095-8956(86)90080-8