vizing造句

• Multigraphs do not in general obey Vizing's theorem.
• Vizing was born in Kiev on March 25, 1937.
• Since Vizing proposed his conjecture, many mathematicians have worked on it, with partial results described below.
• Vizing's conjecture is also known to hold for cycles and for graphs with domination number two.
• According to Vizing's theorem every cubic graph needs either three or four colors for an edge coloring.
• There exist infinite families of graph products for which the bound of Vizing's conjecture is exactly met.
• By Vizing's theorem, the number of colors needed to edge color a simple graph is either its maximum degree or.
• It is possible for the domination number of a product to be much larger than the bound given by Vizing's conjecture.
• From 1976, Vizing stopped working on graph theory and studied problems of scheduling instead, only returning to graph theory again in 1995.
• For instance, Shannon's and Vizing's theorems relating the degree of a graph to its chromatic index both generalize straightforwardly to infinite graphs.
• For graphs of maximum degree three, is always exactly two, so in this case the bound matches the bound given by Vizing's theorem.
• An extension of Brooks'theorem to total coloring, stating that the total chromatic number is at most ? + 2, has been conjectured by Mehdi Behzad and Vizing.
• 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.
• The degree of a graph also appears in upper bounds for other types of coloring; for edge coloring, the result that the chromatic index is at most ? + 1 is Vizing's theorem.
• Although Vizing's theorem is now standard material in many graph theory textbooks, Vizing had trouble publishing the result initially, and his paper on it appears in an obscure journal, " Diskret.
• Although Vizing's theorem is now standard material in many graph theory textbooks, Vizing had trouble publishing the result initially, and his paper on it appears in an obscure journal, " Diskret.
• It has been conjectured ( combining Vizing's theorem and Brooks'theorem ) that any graph has a total coloring in which the number of colors is at most the maximum degree plus two, but this remains unproven.
• If these conjectures are true, it would be possible to compute a number that is never more than one off from the chromatic index in the multigraph case, matching what is known via Vizing's theorem for simple graphs.
• These graphs can be used to generate examples in which the bound of Vizing's conjecture, an unproven inequality between the domination number of the graphs in a different graph product, the cartesian product of graphs, is exactly met.
• The result now known as Vizing's theorem, published in 1964 when Vizing was working in Novosibirsk, states that the edges of any graph with at most ? edges per vertex can be colored using at most ? + 1 colors.