197 research outputs found
The Structure of the 2-factor Transfer Digraph common for Thin Cylinder, Torus and Klein Bottle Grid Graphs
We prove that the transfer digraph needed for the
enumeration of 2-factors in the thin cylinder , torus
and Klein bottle (all grid graphs of the fixed width and with vertices), when is odd, has only two components of order
which are isomorphic. When is even, has components which orders can be expressed via
binomial coefficients and all but one of the components are bipartite digraphs.
The proof is based on the application of recently obtained results concerning
the related transfer digraph for linear grid graphs (rectangular, thick
cylinder and Moebius strip).Comment: 11 pages, 5 figures. arXiv admin note: text overlap with
arXiv:2212.0031
Graph Theory
Highlights of this workshop on structural graph theory included new developments on graph and matroid minors, continuous structures arising as limits of finite graphs, and new approaches to higher graph connectivity via tree structures
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