Eulertur

Eulertur

1. (graph theory) Eulerian trail
   • year unknown, K. Jess, J. Skott, H.C. Hansen og J. Schou, Kristine Jess, Matematik for Laererstuderende, Samfundslitteratur →ISBN, page 355

     1) Hvis der findes en lukket Eulertur gennem grafen G, så har alle knudepunkter i G lige valens. 2) Hvis alle punkter i G har lige valens, så findes der en lukket Eulertur gennem grafen.

     1) If there exists a closed Eulerian trail through the graph G, then all nodes in G have even degree. 2) If all nodes in G have even degree, then there exists a closed Eulerian trail through the graph.

   • 2007, Matematik for lærerstuderende : ypsilon : basisbog, Samfundslitteratur, →ISBN, page 47:

     Euler havde store vanskeligheder med at gå en Eulertur, ikke mindst hvis han ville starte og slutte i sit hjem - altså gå en lukket Eulertur.

     Euler had great difficulties devising an Eulerian trail, not the least if he wanted to start and end in his home - that is, walk a closed Eulerian trail.

   • 2005, Gyldendals Minilex. Matematik, Gyldendal Uddannelse, →ISBN, page 104:

     Det ville svare til, at nedenstående graf har en ▻Eulertur, hvilket den ikke har, idet ikke hvert hjørne har lige valens: ...

     This would be equivalent to saying that the graph below has an ▻Eulerian trail, which it does not, as not every node has even degree: ...

• Eulergraf