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3,381
List total colorings of graphs
, 1996
"... We introduce the concept of list total colorings and prove that every ..."
Algorithms for the Total Colorings of Graphs
, 2002
"... This thesis presents efficient algorithms for finding total colorings of graphs. A total coloring of a graph G is a coloring of all vertices and edges of G such that any two adjacent vertices receive different colors, any two adjacent edges receive different colors, and any edge receives a color dif ..."
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This thesis presents efficient algorithms for finding total colorings of graphs. A total coloring of a graph G is a coloring of all vertices and edges of G such that any two adjacent vertices receive different colors, any two adjacent edges receive different colors, and any edge receives a color
Circular Total Colorings Of Graphs
, 2002
"... A (k; d)total coloring (k; d 2 IN, k 2d) of a graph G is an assignment c of colors f0; 1; : : : ; k 1g to the vertices and edges of G such that d jc(x i ) c(x j )j k d whenever x i and x j are two adjacent edges, two adjacent vertices or an edge incident to a vertex. The circular total chrom ..."
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Cited by 2 (0 self)
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A (k; d)total coloring (k; d 2 IN, k 2d) of a graph G is an assignment c of colors f0; 1; : : : ; k 1g to the vertices and edges of G such that d jc(x i ) c(x j )j k d whenever x i and x j are two adjacent edges, two adjacent vertices or an edge incident to a vertex. The circular total
On interval total colorings of bipartite graphs
, 2009
"... An interval total t coloring of a graph G is a total coloring of with colors 1, such that at least one vertex or edge of is colored by color G 2, , t… G, 1, 2,,i i t = …, and the edges incident to each vertex together with are colored by consecutive colors, where is the degree of the vertex in. I ..."
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Cited by 1 (1 self)
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An interval total t coloring of a graph G is a total coloring of with colors 1, such that at least one vertex or edge of is colored by color G 2, , t… G, 1, 2,,i i t = …, and the edges incident to each vertex together with are colored by consecutive colors, where is the degree of the vertex in
Totalcoloring of plane graphs with maximum degree nine
 SIAM J. DISCRETE MATH
, 2008
"... The central problem of the totalcolorings is the totalcoloring conjecture, which asserts that every graph of maximum degree Δ admits a (Δ + 2)totalcoloring. Similar to edgecolorings—with Vizing’s edgecoloring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum degr ..."
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Cited by 4 (1 self)
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The central problem of the totalcolorings is the totalcoloring conjecture, which asserts that every graph of maximum degree Δ admits a (Δ + 2)totalcoloring. Similar to edgecolorings—with Vizing’s edgecoloring conjecture—this bound can be decreased by 1 for plane graphs of higher maximum
List total colorings of seriesparallel graphs
 Journal of Discrete Algorithms
, 2005
"... Abstract A total coloring of a graph G is a coloring of all elements of G, i.e., vertices and edges, in such a way that no two adjacent or incident elements receive the same color. Let L(x) be a set of colors assigned to each element x of G. Then a list total coloring of G is a total coloring such ..."
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Cited by 4 (0 self)
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Abstract A total coloring of a graph G is a coloring of all elements of G, i.e., vertices and edges, in such a way that no two adjacent or incident elements receive the same color. Let L(x) be a set of colors assigned to each element x of G. Then a list total coloring of G is a total coloring
On the total coloring of graphs embeddable in surfaces
 J London Math Soc
"... The paper shows that any graph G with the maximum degree D(G) & 8, which is embeddable in a surface R of Euler characteristic v(R) & 0, is totally (D(G)›2)colorable. In general, it is shown that any graph G which is embeddable in a surface R and satisfies the maximum degree D(G) & (20}9 ..."
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Cited by 3 (0 self)
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The paper shows that any graph G with the maximum degree D(G) & 8, which is embeddable in a surface R of Euler characteristic v(R) & 0, is totally (D(G)›2)colorable. In general, it is shown that any graph G which is embeddable in a surface R and satisfies the maximum degree D(G) & (20
A STUDY OF THE TOTAL COLORING OF GRAPHS
, 2012
"... This Doctoral Dissertation is brought to you for free and open access by ThinkIR: The University of Louisville's Institutional Repository. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of ThinkIR: The University of Louisville's Ins ..."
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This Doctoral Dissertation is brought to you for free and open access by ThinkIR: The University of Louisville's Institutional Repository. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of ThinkIR: The University of Louisville's Institutional Repository. This title appears here courtesy of the author, who has retained all other copyrights. For more information, please contact
Vertex, edge, and totalcolorings of Sierpińskilike graphs
, 2006
"... Vertexcolorings, edgecolorings and totalcolorings of the Sierpiński gasket graphs Sn, the Sierpiński graphs S(n,k), graphs S + (n,k), and graphs S ++ (n,k) are considered. In particular, χ ′ ′ (Sn), χ ′ (S(n,k)), χ(S + (n,k)), χ(S ++ (n,k)), χ ′ (S + (n,k)), and χ ′ (S ++ (n,k)) are determined. ..."
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Vertexcolorings, edgecolorings and totalcolorings of the Sierpiński gasket graphs Sn, the Sierpiński graphs S(n,k), graphs S + (n,k), and graphs S ++ (n,k) are considered. In particular, χ ′ ′ (Sn), χ ′ (S(n,k)), χ(S + (n,k)), χ(S ++ (n,k)), χ ′ (S + (n,k)), and χ ′ (S ++ (n,k)) are determined.
Results 1  10
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3,381