For many problems in edge coloring, simple graphs behave differently from multigraphs, and additional care is needed to extend theorems about edge colorings of simple graphs to the multigraph case.
22.
In fact, Fred Galvin proved the Dinitz theorem as a special case of his theorem stating that the list chromatic index of any bipartite multigraph is equal to its chromatic index.
23.
:Use different title such as MultiGraph ( medical foundation ) or something else that follows the WP : NC, and place a disambiguation note on top of the Multigraph article.
24.
:Use different title such as MultiGraph ( medical foundation ) or something else that follows the WP : NC, and place a disambiguation note on top of the Multigraph article.
25.
A version of Vizing's theorem states that every multigraph with maximum degree \ Delta and multiplicity \ mu may be colored using at most \ Delta + \ mu colors.
26.
I encountered the term " Multigraph ( orthography ) " today for the first time, along with its collateral meanings such as Digraph ( orthography ) and Trigraph ( orthography ).
27.
Is there any " official " or standard term for a set of letters that function independently in a specific word, even though they're normally used as a multigraph?
28.
Make the input multigraph Eulerian by adding a new vertex connected by an edge to every odd-degree vertex, find an Euler tour, and choose an orientation for the tour.
29.
Conversely, any embedding of a connected multigraph " G " on an oriented closed surface defines a unique rotation system having " G " as its underlying multigraph.
30.
Conversely, any embedding of a connected multigraph " G " on an oriented closed surface defines a unique rotation system having " G " as its underlying multigraph.
