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How to find the spanning elementary subgraphs of a given graph

consider the following definition: A subgraph $H$ of a graph $G$ is called an elementary subgraph if each component of $H$ is either an edge ( $K_{2}$ ) or a cycle of length at least $3$. A spanning elementary subgraph is a subgraph having all components either path(i.e. $K_{2}$) or cycles and verex set is same as those of $G$. for example consider the graph $C_{4}$ with $V(G)$={1,2,3,4}. then it has 3 spanning elementary subgraphs two edge components namely {12,34};{14,23} and the whole cycle itself.The cycle is named in anticlockwise direction. Now my problem is: Consider the following code: G=graphs.EmptyGraph() G.add_edges([(1,2),(2,3),(3,4),(4,5),(5,1),(6,5),(6,8),(8,9),(7,9),(7,6),(7,10),(10,11),(10,12),(11,12)]) G.show() Can we have a sage code that gives all possible spanning subgraphs of this graph.

How to find the spanning elementary subgraphs of a given graph

consider the following definition: A subgraph $H$ of a graph $G$ is called an elementary subgraph if each component of $H$ is either an edge ( $K_{2}$ ) or a cycle of length at least $3$. A spanning elementary subgraph is a subgraph having all components either path(i.e. $K_{2}$) or cycles and verex set is same as those of $G$. for example consider the graph $C_{4}$ with $V(G)$={1,2,3,4}. then it has 3 spanning elementary subgraphs two edge components namely {12,34};{14,23} and the whole cycle itself.The cycle is named in anticlockwise direction. Now my problem is: Consider the following code: G=graphs.EmptyGraph() G.add_edges([(1,2),(2,3),(3,4),(4,5),(5,1),(6,5),(6,8),(8,9),(7,9),(7,6),(7,10),(10,11),(10,12),(11,12)]) G.show() code:

G=graphs.EmptyGraph()

G.add_edges([(1,2),(2,3),(3,4),(4,5),(5,1),(6,5),(6,8),(8,9),(7,9),(7,6),(7,10),(10,11),(10,12),(11,12)])

G.show()

Can we have a sage code that gives all possible spanning subgraphs of this graph.

How to find the spanning elementary subgraphs of a given graph

consider the following definition: A subgraph $H$ of a graph $G$ is called an elementary subgraph if each component of $H$ is either an edge ( $K_{2}$ ) or a cycle of length at least $3$. A spanning elementary subgraph is a subgraph having all components either path(i.e. $K_{2}$) or cycles and verex set is same as those of $G$. for example consider the graph $C_{4}$ with $V(G)$={1,2,3,4}. then it has 3 spanning elementary subgraphs two edge components namely {12,34};{14,23} and the whole cycle itself.The cycle is named in anticlockwise direction. Now my problem is: Consider the following code:

G=graphs.EmptyGraph()

G.add_edges([(1,2),(2,3),(3,4),(4,5),(5,1),(6,5),(6,8),(8,9),(7,9),(7,6),(7,10),(10,11),(10,12),(11,12)])

G.show()

G=graphs.EmptyGraph()
G.add_edges([(1,2),(2,3),(3,4),(4,5),(5,1),(6,5),(6,8),(8,9),(7,9),(7,6),(7,10),(10,11),(10,12),(11,12)])
G.show()

Can we have a sage code that gives all possible spanning subgraphs of this graph.

How to find the spanning elementary subgraphs of a given graph

consider the following definition: A subgraph $H$ of a graph $G$ is called an elementary subgraph if each component of $H$ is either an edge ( $K_{2}$ ) or a cycle of length at least $3$. A spanning elementary subgraph is a subgraph having all components either path(i.e. $K_{2}$) or cycles and verex set is same as those of $G$. for example consider the graph $C_{4}$ with $V(G)$={1,2,3,4}. then it has 3 spanning elementary subgraphs two edge components namely {12,34};{14,23} and the whole cycle itself.The cycle is named in anticlockwise direction. Now my problem is: Consider the following code:

G=graphs.EmptyGraph()
G.add_edges([(1,2),(2,3),(3,4),(4,5),(5,1),(6,5),(6,8),(8,9),(7,9),(7,6),(7,10),(10,11),(10,12),(11,12)])
G.show()

Can we have a sage code that gives all possible spanning subgraphs of this graph.