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Ars Combinatoria, 2023
For a graph G and a positive integer k , a royal k -edge coloring of G is an assignment of nonempty subsets of the set { 1 , 2 , … , k } to the edges of G that gives rise to a proper vertex coloring in which the color assigned to each vertex v is the union of the sets of colors of the edges incident with v .
Gary Chartrand +2 more
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For a graph G and a positive integer k , a royal k -edge coloring of G is an assignment of nonempty subsets of the set { 1 , 2 , … , k } to the edges of G that gives rise to a proper vertex coloring in which the color assigned to each vertex v is the union of the sets of colors of the edges incident with v .
Gary Chartrand +2 more
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Cut-Colorings in Coloring Graphs
Graphs and Combinatorics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Prateek Bhakta +5 more
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On Indicated Coloring of Graphs
Graphs and Combinatorics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Pandiyaraj +2 more
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Combinatorica, 1990
In this paper multigraphs \(G=(V,E)\) without loops are under consideration. They are assigned edge colourings satisfying the following two conditions: (i) Each colour appears at each vertex v no more than f(v) times. (ii) Each colour appears at each set of multiple edges joining vertices v and w no more than g(vw) times.
Shin-Ichi Nakano +2 more
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In this paper multigraphs \(G=(V,E)\) without loops are under consideration. They are assigned edge colourings satisfying the following two conditions: (i) Each colour appears at each vertex v no more than f(v) times. (ii) Each colour appears at each set of multiple edges joining vertices v and w no more than g(vw) times.
Shin-Ichi Nakano +2 more
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Graphs and Combinatorics, 2010
The chromatic number of a graph \(G\) is written \(\chi(G)\). A proper \(k\)-coloring of a graph \(G\) with color classes \(V_1, \dots, V_k\) is a {\parindent=6mm \begin{itemize}\item[-] \(k\)-fall coloring if each vertex in \(V_i\) is adjacent to at least one vertex in \(V_j\), \(j\not= i\); the last, respectively, largest positive integer \(k\) for ...
Rangaswami Balakrishnan +1 more
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The chromatic number of a graph \(G\) is written \(\chi(G)\). A proper \(k\)-coloring of a graph \(G\) with color classes \(V_1, \dots, V_k\) is a {\parindent=6mm \begin{itemize}\item[-] \(k\)-fall coloring if each vertex in \(V_i\) is adjacent to at least one vertex in \(V_j\), \(j\not= i\); the last, respectively, largest positive integer \(k\) for ...
Rangaswami Balakrishnan +1 more
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Mathematical Logic Quarterly, 1995
AbstractThe problem of when a recursive graph has a recursive k‐coloring has been extensively studied by Bean, Schmerl, Kierstead, Remmel, and others. In this paper, we study the polynomial time analogue of that problem. We develop a number of negative and positive results about colorings of polynomial time graphs.
Jeffrey B. Remmel, Douglas A. Cenzer
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AbstractThe problem of when a recursive graph has a recursive k‐coloring has been extensively studied by Bean, Schmerl, Kierstead, Remmel, and others. In this paper, we study the polynomial time analogue of that problem. We develop a number of negative and positive results about colorings of polynomial time graphs.
Jeffrey B. Remmel, Douglas A. Cenzer
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Graphs and Combinatorics, 2014
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Houcine Boumediene Merouane +3 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Houcine Boumediene Merouane +3 more
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24th Annual Symposium on Foundations of Computer Science (sfcs 1983), 1983
The following computational problem was initiated by \textit{U. Manber} and \textit{M. Tompa} [Proc. 22nd Annual Symposium on the Foundations of Computer Science (1981)]: Given a graph \(G=(V,E)\) and a real function \(f: V\to {\mathbb{R}}\) which is a proposed vertex coloring. Decide whether f is a proper vertex coloring of G. The elementary steps are
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The following computational problem was initiated by \textit{U. Manber} and \textit{M. Tompa} [Proc. 22nd Annual Symposium on the Foundations of Computer Science (1981)]: Given a graph \(G=(V,E)\) and a real function \(f: V\to {\mathbb{R}}\) which is a proposed vertex coloring. Decide whether f is a proper vertex coloring of G. The elementary steps are
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Fundamenta Informaticae, 2012
Dynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's,
Piotr Borowiecki, Elzbieta Sidorowicz
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Dynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's,
Piotr Borowiecki, Elzbieta Sidorowicz
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Graphs and Combinatorics, 1998
For a family \(\mathcal H\) of graphs, the \(\mathcal H\)-restricted chromatic number of \(G\), \(\chi_{\mathcal H ^ *}(G)\), denotes the minimum \(k\) such that \(G\) admits a partition of the vertices into \(k\) parts, each of which induces a disjoint union of graphs from \(\mathcal H\).
Walter A. Deuber, Xuding Zhu
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For a family \(\mathcal H\) of graphs, the \(\mathcal H\)-restricted chromatic number of \(G\), \(\chi_{\mathcal H ^ *}(G)\), denotes the minimum \(k\) such that \(G\) admits a partition of the vertices into \(k\) parts, each of which induces a disjoint union of graphs from \(\mathcal H\).
Walter A. Deuber, Xuding Zhu
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