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Colorful path detection in vertex-colored temporal
Network Science, 2023AbstractFinding paths is a fundamental problem in graph theory and algorithm design due to its many applications. Recently, this problem has been considered on temporal graphs, where edges may change over a discrete time domain. The analysis of graphs has also taken into account the relevance of vertex properties, modeled by assigning to vertices ...
Dondi, Riccardo +1 more
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Maximum Colorful Cycles in Vertex-Colored Graphs
2018In this paper, we study the problem of finding a maximum colorful cycle a vertex-colored graph. Specifically, given a graph with colored vertices, the goal is to find a cycle containing the maximum number of colors. We aim to give a dichotomy overview on the complexity of the problem.
Italiano, Giuseppe +3 more
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Maximum Colorful Cliques in Vertex-Colored Graphs
2018In this paper we study the problem of finding a maximum colorful clique in vertex-colored graphs. Specifically, given a graph with colored vertices, we wish to find a clique containing the maximum number of colors. Note that this problem is harder than the maximum clique problem, which can be obtained as a special case when each vertex has a different ...
Italiano, Giuseppe +3 more
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Distributed Game-Theoretic Vertex Coloring
2010We exploit the game-theoretic ideas presented in [12] to study the vertex coloring problem in a distributed setting. The vertices of the graph are seen as players in a suitably defined strategic game, where each player has to choose some color, and the payoff of a vertex is the total number of players that have chosen the same color as its own.
CHATZIGIANNAKIS, IOANNIS +3 more
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Tropical Paths in Vertex-Colored Graphs
Journal of Combinatorial Optimization, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cohen, Johanne +5 more
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Vertex‐distinguishing edge colorings of graphs
Journal of Graph Theory, 2002AbstractWe consider lower bounds on the the vertex‐distinguishing edge chromatic number of graphs and prove that these are compatible with a conjecture of Burris and Schelp 8. We also find upper bounds on this number for certain regular graphs G of low degree and hence verify the conjecture for a reasonably large class of such graphs.
Balister, P. N. +2 more
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2016
In Chap. 2 and 3, we described two edge colorings that give rise to two vertex colorings, one in terms of sets of colors and the other in terms of multisets. Now, in this chapter and the next, the situation is reversed, as we describe vertex colorings that give rise to edge colorings.
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In Chap. 2 and 3, we described two edge colorings that give rise to two vertex colorings, one in terms of sets of colors and the other in terms of multisets. Now, in this chapter and the next, the situation is reversed, as we describe vertex colorings that give rise to edge colorings.
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Max-Coloring of Vertex-Weighted Graphs
Graphs and Combinatorics, 2015A proper vertex coloring of a graph \(G\) is a partition \(\{A_1, \dots, A_k\}\) of the vertex set \(V(G)\) into stable sets. For a graph \(G\) with a positive vertex weight \(c: V(G) \to (0, \infty)\), denoted by \((G, c)\), let \(\chi (G, c)\) be the minimum value of \(\sum_{i = 1}^k \max_{v \in A_i}c(v)\) over all proper vertex colorings \(\{A_1 ...
Hsiang-Chun Hsu, Gerard Jennhwa Chang
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Adjacent Vertex Reducible Vertex-Total Coloring of Graphs
2009 International Conference on Computational Intelligence and Software Engineering, 2009Let G =( V, E) be a simple graph,k (1 ≤ k ≤ Δ(G )+1 ) is a positive integer. f is a mapping from V (G) ∪ E(G) to {1, 2, ··· ,k } such that ∀uv ∈ E(G),f (u) = f (v) and C(u )= C(v) if d(u )= d(v),we say that f is the adjacent vertex reducible vertex-total coloring of G.
Enqiang Zhu +5 more
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On N2-vertex coloring of graphs
Discrete Mathematics, Algorithms and Applications, 2018Let [Formula: see text] be a graph. A vertex coloring [Formula: see text] of [Formula: see text] is called [Formula: see text]-vertex coloring if [Formula: see text] for every vertex [Formula: see text] of [Formula: see text], where [Formula: see text] is the set of colors of vertices adjacent to [Formula: see text].
S. Akbari +3 more
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