Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Total_coloring> ?p ?o }
Showing triples 1 to 50 of
50
with 100 triples per page.
- Total_coloring abstract "In graph theory, total coloring is a type of graph coloring on the vertices and edges of a graph.When used without any qualification, a total coloring is always assumed to be proper in the sense that no adjacent edges and no edge and its endvertices are assigned the same color.The total chromatic number χ″(G) of a graph G is the least number of colors needed in any total coloring of G.The total graph T = T(G) of a graph G is a graph such that (i) the vertex set of T corresponds to the vertices and edges of G and (ii) two vertices are adjacent in T if and only if their corresponding elements are either adjacent or incident in G.Then total coloring becomes a (proper) vertex coloring of the total graph.Some properties of χ″(G): χ″(G) ≥ Δ(G) + 1. χ″(G) ≤ Δ(G) + 1026. (Molloy, Reed 1998) χ″(G) ≤ Δ(G) + 8 ln8(Δ(G)) for sufficiently large Δ(G). (Hind, Molloy, Reed 1998) χ″(G) ≤ ch′(G) + 2.Here Δ(G) is the maximum degree; and ch′(G), the edge choosability.Total coloring arises naturally since it is simply a mixture of vertex and edge colorings.The next step is to look for any Brooks-typed or Vizing-typed upper bound on the total chromatic number in terms of maximum degree.It turns out that the total coloring version of maximum degree upper bound is a difficult problem and has eluded mathematicians for 40 years.The most well-known speculation is the following.Total coloring conjecture. (Behzad, Vizing)χ″(G) ≤ Δ(G) + 2.Apparently, the term "total coloring" and the statement of total coloring conjecture were independently introduced by Behzad and Vizing in numerous occasions between 1964 and 1968.See [Jensen, Toft 1995] for details.The conjecture is known to hold for a few important classes of graphs, such as all bipartite graphs and most planar graphs except those with maximum degree 6.The planar case can be completed if Vizing's planar graph conjecture is true.Also, if the list coloring conjecture is true, then χ″(G) ≤ Δ(G) + 3.Results related to total coloring have been obtained.For example, Kilakos and Reed (1993) proved that the fractional chromatic number of the total graph of a graph G is at most Δ(G) + 2.Some properties of the line graph and the total graph:T = T(G) is Eulerian if and only if the line graph L(G) is Eulerian.".
- Total_coloring thumbnail Total_coloring_foster_cage.svg?width=300.
- Total_coloring wikiPageID "690702".
- Total_coloring wikiPageLength "4279".
- Total_coloring wikiPageOutDegree "24".
- Total_coloring wikiPageRevisionID "680976208".
- Total_coloring wikiPageWikiLink Bipartite_graph.
- Total_coloring wikiPageWikiLink Brooks_theorem.
- Total_coloring wikiPageWikiLink Category:Graph_coloring.
- Total_coloring wikiPageWikiLink Edge_(graph_theory).
- Total_coloring wikiPageWikiLink Edge_coloring.
- Total_coloring wikiPageWikiLink Eulerian.
- Total_coloring wikiPageWikiLink Foster_cage.
- Total_coloring wikiPageWikiLink Fractional_coloring.
- Total_coloring wikiPageWikiLink Glossary_of_graph_theory.
- Total_coloring wikiPageWikiLink Graph_(mathematics).
- Total_coloring wikiPageWikiLink Graph_coloring.
- Total_coloring wikiPageWikiLink Graph_theory.
- Total_coloring wikiPageWikiLink Line_graph.
- Total_coloring wikiPageWikiLink List_edge-coloring.
- Total_coloring wikiPageWikiLink List_of_things_named_after_Leonhard_Euler.
- Total_coloring wikiPageWikiLink Mehdi_Behzad.
- Total_coloring wikiPageWikiLink Planar_graph.
- Total_coloring wikiPageWikiLink SIAM_Journal_on_Computing.
- Total_coloring wikiPageWikiLink Vadim_G._Vizing.
- Total_coloring wikiPageWikiLink Vertex_(graph_theory).
- Total_coloring wikiPageWikiLink File:Total_coloring_foster_cage.svg.
- Total_coloring wikiPageWikiLinkText "''k''-total-chromatic graph".
- Total_coloring wikiPageWikiLinkText "(proper) ''k''-total-coloring".
- Total_coloring wikiPageWikiLinkText "Total coloring".
- Total_coloring wikiPageWikiLinkText "total chromatic number".
- Total_coloring wikiPageWikiLinkText "total coloring conjecture".
- Total_coloring wikiPageWikiLinkText "total coloring".
- Total_coloring hasPhotoCollection Total_coloring.
- Total_coloring wikiPageUsesTemplate Template:Cite_journal.
- Total_coloring subject Category:Graph_coloring.
- Total_coloring hypernym Graph.
- Total_coloring type Software.
- Total_coloring comment "In graph theory, total coloring is a type of graph coloring on the vertices and edges of a graph.When used without any qualification, a total coloring is always assumed to be proper in the sense that no adjacent edges and no edge and its endvertices are assigned the same color.The total chromatic number χ″(G) of a graph G is the least number of colors needed in any total coloring of G.The total graph T = T(G) of a graph G is a graph such that (i) the vertex set of T corresponds to the vertices and edges of G and (ii) two vertices are adjacent in T if and only if their corresponding elements are either adjacent or incident in G.Then total coloring becomes a (proper) vertex coloring of the total graph.Some properties of χ″(G): χ″(G) ≥ Δ(G) + 1. ".
- Total_coloring label "Total coloring".
- Total_coloring sameAs Totalfärbung.
- Total_coloring sameAs رنگآمیزی_کامل_گراف.
- Total_coloring sameAs m.0332mq.
- Total_coloring sameAs Тотальная_раскраска.
- Total_coloring sameAs Тотальна_розмальовка.
- Total_coloring sameAs Q7828102.
- Total_coloring sameAs Q7828102.
- Total_coloring wasDerivedFrom Total_coloring?oldid=680976208.
- Total_coloring depiction Total_coloring_foster_cage.svg.
- Total_coloring isPrimaryTopicOf Total_coloring.