That is if H is a Minor of a graph G through any property of H can we conclude G as Eulerian if it is under certain conditions.
Minor of a graph G is obtained by contracting the edges of G. But eulerian graph is a graph with all the vertices of even degree. There is no connection in between them.
Does the Eulerian nature has a hereditary property on the number contractions we make and the type of graph we take under certain condition only i mean.
Like minors of planar graphs are always planar.
There is an if and only if condition
If all vertices of a connected graph are of even degree if and only if it contains a Euler circuit. In term the graph is Eulerian.
As far a edge contraction we mean merging the two nodes at either end of an edge then remove the self loop's and multiple edges we can even put two non-adjacent vertices too.
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