An Euler Circuit is a circuit that crosses every edge exactly once without repeating. A graph...

An Euler Circuit is a circuit that crosses every edge exactly once without repeating. A graph has an Euler Circuit if and only if (a) the graph is connected and (b) the degree of every vertex is even. Find a lower bound for the time complexity of all algorithms that determine if a graph has an Euler Circuit. In which of the three general categories discussed in Section 9.3 does this problem belong? Justify your answer.

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venereology answered 13 hours ago

An eulerian walk is a sequence of vertices in a graph such that every edge is...

An eulerian walk is a sequence of vertices in a graph such that every edge is traversed exactly once. It differs from an eulerian circuit in that the starting and ending vertex don’t have to be the same. Prove that if a graph is connected and has at most two vertices of odd degree, then it has an eulerian walk.

We say a graph is k-regular if every vertex has degree exactly k. In each of...

We say a graph is k-regular if every vertex has degree exactly k. In each of the following either give a presentation of the graph or show that it does not exist. 1) 3-regular graph on 2018 vertices. 2) 3-regular graph on 2019 vertices.

Without using the Tutte-Berge formula, prove that every cubic graph with at most two bridges contains...

Without using the Tutte-Berge formula, prove that every cubic graph with at most two bridges contains a perfect matching.

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An Euler Circuit is a circuit that crosses every edge exactly once without repeating. A graph...

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An eulerian walk is a sequence of vertices in a graph such that every edge is...

We say a graph is k-regular if every vertex has degree exactly k. In each of...

Without using the Tutte-Berge formula, prove that every cubic graph with at most two bridges contains...