query: Prove that for any connected graph, there exists a closed walk that visits every edge exactly twice.
positive_passages.docid: 148438
positive_passages.text: Show that every nontrivial connected graph $G$ has a closed spanning walk that contains every edge of $G$ exactly twice.
negative_passages.docid: 86271
negative_passages.text: Spanning Trees: Prove if $e_1$ is an edge in $X$ that isn't in $Y$, then there exists an edge ...
negative_passages.docid: 72556
negative_passages.text: Is the closure of path-connected set path connected?
negative_passages.docid: 43555
negative_passages.text: Show that a finite regular bipartite graph has a perfect matching
negative_passages.docid: 4602
negative_passages.text: Outline of a proof that $\mathbb{R}^2 - A$ where A is countable is path-connected
negative_passages.docid: 27407
negative_passages.text: every planar graph can be expressed as a union of five edge-disjoint forests
negative_passages.docid: 6429
negative_passages.text: prove that a connected graph with $n$ vertices has at least $n-1$ edges
negative_passages.docid: 71154
negative_passages.text: Why a complete graph has $\frac{n(n-1)}{2}$ edges?
negative_passages.docid: 107193
negative_passages.text: Exact probability of random graph being connected
negative_passages.docid: 23965
negative_passages.text: Function which preserves closed-boundedness and path-connectedness continuous?
negative_passages.docid: 4061
negative_passages.text: Proving there are infinitely many pairs of square-full consecutive integers
negative_passages.docid: 140199
negative_passages.text: Proof that disjoint cycles commute
negative_passages.docid: 39753
negative_passages.text: Proving that in a simple graph with $n$ vertices, two vertices have the same degree
negative_passages.docid: 67887
negative_passages.text: Prove that a graph on $n$ vertices with girth $g$ has at most $\frac{g}{g-2}(n-2)$ edges
negative_passages.docid: 108394
negative_passages.text: Proof of that every interval is connected
negative_passages.docid: 49879
negative_passages.text: A bipartite graph with a perfect matching has a vertex with each edge contained in a perfect matching
negative_passages.docid: 27661
negative_passages.text: The closed graph theorem in topology