80 research outputs found
The chromatic numbers of double coverings of a graph
If we fix a spanning subgraph of a graph , we can define a chromatic
number of with respect to and we show that it coincides with the
chromatic number of a double covering of with co-support . We also find
a few estimations for the chromatic numbers of with respect to .Comment: 10 page
On Stable embeddability of partitions
Several natural partial orders on integral partitions, such as the
embeddability, the stable embeddability, the bulk embeddability and the
supermajorization, raise in the quantum computation, bin-packing and matrix
analysis. We find the implications between these partial orders. For integral
partitions whose entries are all powers of a fixed number , we show that the
embeddability is completely determined by the supermajorization order and we
find an algorithm to determine the stable embeddability.Comment: 10 page
Enumerations of finite topologies associated with a finite graph
The number of topologies and non-homeomorphic topologies on a fixed finite
set are now known up to , but still no complete formula yet
(Sloane). There are one to one correspondence among topologies, preorder and
digraphs. In this article, we enumerate topologies and non-homeomorphic
topologies whose underlying graph is a given finite graph.Comment: 2 figure
Enumeration of the BranchedmZp-Coverings of Closed Surfaces
AbstractIn this paper, we enumerate the equivalence classes of regular branched coverings of surfaces whose covering transformation groups are the direct sum of m copies of Zp, p prime
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