Results 11 to 20 of about 152,670 (312)
Generalized Fractional Total Colorings of Complete Graph
Discussiones Mathematicae Graph Theory, 2013 An additive and hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be two additive and hereditary graph properties and let r, s be integers such that r ≥ s Then an fractional (P,
Karafová Gabriela
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Complete Acyclic Colorings [PDF]
The Electronic Journal of Combinatorics, 2019 We study two parameters that arise from the dichromatic number and the vertex-arboricity in the same way that the achromatic number comes from the chromatic number. The adichromatic number of a digraph is the largest number of colors its vertices can be colored with such that every color induces an acyclic subdigraph but merging any two colors yields a
Stefan Felsner +3 more
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Subset sums, completeness and colorings [PDF]
, 2021 We develop novel techniques which allow us to prove a diverse range of results relating to subset sums and complete sequences of positive integers, including solutions to several longstanding open problems. These include: solutions to the three problems of Burr and Erd s on Ramsey complete sequences, for which Erd s later offered a combined total of \
David Conlon, Jacob Fox, Huy Tuan Pham
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Complete edge-colored permutation graphs
Advances in Applied Mathematics, 2022 Nous introduisons le concept de graphes de permutation complets de couleur d'arête comme des graphes complets qui sont l'union bord-disjonction de graphes de permutation « classiques ». Nous montrons qu'un graphe G=(V,E) est un graphe de permutation complet de couleur de bord si et seulement si chaque sous-graphe monochromatique de G est un graphe de ...
Tom Hartmann +5 more
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Semi-algebraic colorings of complete graphs [PDF]
, 2015 We consider $m$-colorings of the edges of a complete graph, where each color class is defined semi-algebraically with bounded complexity. The case $m = 2$ was first studied by Alon et al., who applied this framework to obtain surprisingly strong Ramsey-type results for intersection graphs of geometric objects and for other graphs arising in ...
Jacob Fox, János Pach, Andrew Suk
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Near-Colorings: Non-Colorable Graphs and NP-Completeness [PDF]
The Electronic Journal of Combinatorics, 2015 A graph $G$ is $(d_1,...,d_l)$-colorable if the vertex set of $G$ can be partitioned into subsets $V_1,\ldots ,V_l$ such that the graph $G[V_i]$ induced by the vertices of $V_i$ has maximum degree at most $d_i$ for all $1 \leq i \leq l$. In this paper, we focus on complexity aspects of such colorings when $l=2,3$. More precisely, we prove that, for any
Montassier, Mickaël, Ochem, Pascal
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The Coloring Graph of Complete Graphs
The PUMP Journal of Undergraduate Research, 2019 We study the coloring graph of the family of complete graphs and we prove that Cn(Kt) is regular, transitive, and connected when n>t. Also, we study whether Cn(Kt) is distance transitive or strongly regular, and find its diameter.
Haylee Aileen Harris
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On Colorful Edge Triples in Edge-Colored Complete Graphs [PDF]
Graphs and Combinatorics, 2020 AbstractAn edge-coloring of the complete graph $$K_n$$ K n we call F-caring if it leaves no F-subgraph of $$K_n$$ K n monochromatic and at the same time every subset of |V(F)| vertices contains in it at least one completely multicolored version of F. For the first two meaningful cases, when $$F=K_{1,3}$$ F = K 1 , 3 and $$F=P_4$$ F = P 4
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Edge‐colored complete graphs without properly colored even cycles: A full characterization [PDF]
Journal of Graph Theory, 2021 AbstractThe structure of edge‐colored complete graphs containing no properly colored triangles has been characterized by Gallai back in the 1960s. More recently, Cǎda et al. and Fujita et al. independently determined the structure of edge‐colored complete bipartite graphs containing no properly colored .
Ruonan Li +3 more
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Properly colored Hamilton cycles in edge-colored complete graphs [PDF]
Random Structures and Algorithms, 1997 For any \(\varepsilon>0\) it is shown that if the edges of a sufficiently large complete graph \(K_n\) are colored such that no vertex is adjacent to more than \((1-1/\sqrt 2-\varepsilon)n\) edges, then for each \(3\leq k\leq n\), there is a cycle of length \(k\) with consecutive edges of different colors.
Gutin, Gregory, Alon, N.
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