Question regarding union of disjoint 1-factors Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)The complement of spanning trees is covered by a union of cyclesTwo disjoint spanning trees, spanning subgraph with all even degreesFind edge disjoint spanning tree subgraph between A and BLet T be a spanning tree of a connected graph G..Characterization of bicycle graphsSpanning 2-regular subgraphs in even regular graphs.Proving that a 4-regular graph has two edge-disjoint cyclesfactorisations of vertex transitive graphsQuestion regarding the connectedness of spanning 2-regular subgraphsIs every $f(k)$-vertex-connected graph the edge-disjoint union of two $k$-vertex-connected graphs?
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Question regarding union of disjoint 1-factors
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)The complement of spanning trees is covered by a union of cyclesTwo disjoint spanning trees, spanning subgraph with all even degreesFind edge disjoint spanning tree subgraph between A and BLet T be a spanning tree of a connected graph G..Characterization of bicycle graphsSpanning 2-regular subgraphs in even regular graphs.Proving that a 4-regular graph has two edge-disjoint cyclesfactorisations of vertex transitive graphsQuestion regarding the connectedness of spanning 2-regular subgraphsIs every $f(k)$-vertex-connected graph the edge-disjoint union of two $k$-vertex-connected graphs?
$begingroup$
If a connected graph has two edge disjoint 1-factors, then the union of those two 1-factors is always a 2-regular spanning subgraph isn't it?
Moreover, when we consider a 2-regular spanning subgraph, which is formed by the union of two edge disjoint 1-factors and which is also a union of disjoint cycles rather than being a single cycle, then the cycles in the union should be of even length isn't it? Otherwise there will be an edge which does not belong to a disjoint union of 1-factors,right?
Can someone please help me with these two questions?
Thanks a lot in advance.
combinatorics discrete-mathematics graph-theory
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
$endgroup$
add a comment |
$begingroup$
If a connected graph has two edge disjoint 1-factors, then the union of those two 1-factors is always a 2-regular spanning subgraph isn't it?
Moreover, when we consider a 2-regular spanning subgraph, which is formed by the union of two edge disjoint 1-factors and which is also a union of disjoint cycles rather than being a single cycle, then the cycles in the union should be of even length isn't it? Otherwise there will be an edge which does not belong to a disjoint union of 1-factors,right?
Can someone please help me with these two questions?
Thanks a lot in advance.
combinatorics discrete-mathematics graph-theory
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
$endgroup$
add a comment |
$begingroup$
If a connected graph has two edge disjoint 1-factors, then the union of those two 1-factors is always a 2-regular spanning subgraph isn't it?
Moreover, when we consider a 2-regular spanning subgraph, which is formed by the union of two edge disjoint 1-factors and which is also a union of disjoint cycles rather than being a single cycle, then the cycles in the union should be of even length isn't it? Otherwise there will be an edge which does not belong to a disjoint union of 1-factors,right?
Can someone please help me with these two questions?
Thanks a lot in advance.
combinatorics discrete-mathematics graph-theory
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
$endgroup$
If a connected graph has two edge disjoint 1-factors, then the union of those two 1-factors is always a 2-regular spanning subgraph isn't it?
Moreover, when we consider a 2-regular spanning subgraph, which is formed by the union of two edge disjoint 1-factors and which is also a union of disjoint cycles rather than being a single cycle, then the cycles in the union should be of even length isn't it? Otherwise there will be an edge which does not belong to a disjoint union of 1-factors,right?
Can someone please help me with these two questions?
Thanks a lot in advance.
combinatorics discrete-mathematics graph-theory
combinatorics discrete-mathematics graph-theory
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
asked Apr 1 at 13:10
Buddhini AngelikaBuddhini Angelika
13611
13611
add a comment |
add a comment |
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