Cycle double covers and the semi-Kotzig frame
نویسندگان
چکیده
منابع مشابه
Cycle double covers and the semi-Kotzig frame
Let H be a cubic graph admitting a 3-edge-coloring c : E(H) → Z3 such that the edges colored with 0 and μ ∈ {1, 2} induce a Hamilton circuit of H and the edges colored with 1 and 2 induce a 2-factor F . The graph H is semi-Kotzig if switching colors of edges in any even subgraph of F yields a new 3-edge-coloring ofH having the same property as c . A spanning subgraphH of a cubic graph G is call...
متن کاملKotzig frames and circuit double covers
A cubic graph H is called a Kotzig graph if H has a circuit double cover consisting of three Hamilton circuits. It was first proved by Goddyn that if a cubic graph G contains a spanning subgraph H which is a subdivision of a Kotzig graph then G has a circuit double cover. A spanning subgraph H of a cubic graph G is called a Kotzig frame if the contracted graph G/H is even and every non-circuit ...
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Define a graph to be a Kotzig graph if it is m-regular and has an m-edge colouring in which each pair of colours form a Hamiltonian cycle. We show that every cubic graph with spanning subgraph consisting of a subdivision of a Kotzig graph together with even cycles has a cycle double cover, in fact a 6-CDC. We prove this for two other families of graphs similar to Kotzig graphs as well. In parti...
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In this paper we continue our investigations from [HM01] regarding spanning subgraphs which imply the existence of cycle double covers. We prove that if a cubic graph G has a spanning subgraph isomorphic to a subdivision of a bridgeless cubic graph on at most 10 vertices then G has a CDC. A notable result is thus that a cubic graph with a spanning Petersen minor has a CDC, a result also obtaine...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2011.12.001