(k, g)-cages are 3-connected
نویسندگان
چکیده
منابع مشابه
3-Connected {K 1, 3, P 9}-Free Graphs are Hamiltonian-Connected
We investigate pairs of forbidden subgraphs that imply a 3-connected graph is Hamiltonian-connected. In particular we show that the pair {K1,3, P9} is such a pair. As it is known that P10 cannot replace P9, this result is best possible. Further, we show that certain other graphs are not possible.
متن کاملAll Ramsey numbers r ( K 3 , G ) for connected graphs of order 9 Stephan Brandt
We determine the Ramsey numbers r(K3, G) for all 261080 connected graphs of order 9 and further Ramsey numbers of this type for some graphs of order up to 12. Almost all of them were determined by computer programs which are based on a program for generating maximal triangle-free graphs.
متن کاملAn open problem : ( 4 ; g ) - cages with odd g ≥ 5 are tightly superconnected
Interconnection networks form an important area which has received much attention, both in theoretical research and in practice. From theoretical point of view, an interconnection network can be modelled by a graph, where the vertices of the graph represent the nodes of the network and the edges of the graph represent connections between the nodes in the network. Fault tolerance is an important...
متن کاملA note on the upper bound and girth pair of (k;g)-cages
A (k; g)-cage is a k-regular graph of girth g with minimum order. In this work, for all k ≥ 2 and g ≥ 5 odd, we present an upper bound of the order of a (k; g + 1)-cage, which depends on the order of a (k; g)-cage, improving a previous result of Sauer of 1967. We also show that every (k; 11)-cage contains a cycle of length 12, confirming a case of a conjecture of Harary and Kóvacs of 1983.
متن کامل4 FORMALITY OF k - CONNECTED SPACES IN 4 k + 3 AND 4 k + 4 DIMENSIONS GIL
Using the concept of s-formality we are able to extend the bounds of a Theorem of Miller and show that a compact k-connected (4k + 3)or (4k + 4)-manifold with bk+1 = 1 is formal. We study k connected n-manifolds, n = 4k + 3, 4k + 4, with a hard Lefschetzlike property and prove that in this case if bk+1 = 2, then the manifold is formal, while, in 4k+3-dimensions, if bk+1 = 3 all Massey products ...
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: Discrete Mathematics
سال: 1999
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00342-2