Journal ArticleDOI
List Total Colourings of Graphs
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TLDR
The concept of list total colourings is studied and it is proved that every multigraph of maximum degree 3 is 5-total-choosable and the total choice number of a graph is equal to its total chromatic number.Abstract:
We study the concept of list total colourings and prove that every multigraph of maximum degree 3 is 5-total-choosable. We also show that the total choice number of a graph of maximum degree 2 is equal to its total chromatic number.read more
Citations
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Journal ArticleDOI
Graph colorings with local constraints - a survey
TL;DR: This work surveys the literature on those variants of the chromatic number problem where not only a proper coloring has to be found but some further local restrictions are imposed on the color assignment.
Journal ArticleDOI
Colorings of plane graphs: A survey
TL;DR: The only improper coloring discussed is injective coloring (any two vertices having a common neighbor should have distinct colors).
Book ChapterDOI
List colourings of graphs
TL;DR: A list colouring of a graph is a colouring in which each vertex receives a colour from a prescribed list L ( υ ) of colours as discussed by the authors, in which adjacent vertices must receive different colours.
Journal IssueDOI
List-coloring the square of a subcubic graph
Daniel W. Cranston,Seog-Jin Kim +1 more
TL;DR: In this article, it was shown that if G is a planar graph with Δ(G) = 3 and girth G = 9, then χl(G2) ≈ 6.
Posted Content
List-coloring the Square of a Subcubic Graph
Daniel W. Cranston,Seog-Jin Kim +1 more
TL;DR: It is proved that every connected graph (not necessarily planar) with $\Delta(G)=3$ other than the Petersen graph satisfies $\chi_l(G^2)\leq 8$ (and this is best possible).
References
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Journal ArticleDOI
Colorings and orientations of graphs
Noga Alon,Michael Tarsi +1 more
TL;DR: Bounds for the chromatic number and for some related parameters of a graph are obtained by applying algebraic techniques by proving that there is a legal vertex-coloring of G assigning to each vertexv a color fromS(v).
Journal ArticleDOI
The list chromatic index of a bipartite multigraph
TL;DR: This paper generalizes Janssen′s result on complete bipartite graphs Km, n with m ≠ n and answers a question of Dinitz about the list chromatic index.
Journal ArticleDOI
List Edge and List Total Colourings of Multigraphs
TL;DR: It is proved here that if every edgee=uw of a bipartite multigraphGis assigned a list of at least max{d(u),d(w)} colours, then G can be edge-coloured with each edge receiving a colour from its list.
Journal ArticleDOI
The chromatic class of a multigraph
TL;DR: In this article, the authors define a book which, in addition to having a pair of covers interconnected along corresponding edges thereof with a set of leaves therebetween, also has a recess defined therein, adjacent one of the covers, which opens to the outside of the book and is adapted to receive a tape cassette, and/or an enclosure for the same, or the like therein.
Journal ArticleDOI
On the total coloring of certain graphs
TL;DR: In this paper, it was shown that every cubic graph is totally colorable in five colors, and that the total chromatic number of certain graphs can be computed in terms of the number of colors.