Results 21 to 30 of about 139 (132)
Coloring clique-hypergraphs of graphs with no subdivision of \(K_5\)
Theor. Comput. Sci., 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Erfang Shan, Liying Kang
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Applications of hypergraph coloring to coloring graphs not inducing certain trees
Discrete Mathematics, 1996 The authors present a simple result on coloring hypergraphs and use it to obtain bounds on the chromatic number of graphs which do not induce certain trees. Several open problems are discussed.
Hal A. Kierstead, Vojtech Rödl
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New hardness results for graph and hypergraph colorings.
Electron. Colloquium Comput. Complex., 2016 Finding a proper coloring of a t-colorable graph G with t colors is a classic NP-hard problem when t >= 3. In this work, we investigate the approximate coloring problem in which the objective is to find a proper c-coloring of G where c >= t. We show that for all t >= 3, it is NP-hard to find a c-coloring when c
Brakensiek, Joshua +1 more
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Color-critical Graphs and Hereditary Hypergraphs
CoRR, 2019 A quick proof of Gallai's celebrated theorem on color-critical graphs is given from Gallai's simple, ingenious lemma on factor-critical graphs, in terms of partitioning the vertex-set into a minimum number of hyperedges of a hereditary hypergraph, generalizing the chromatic number.
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Erdős‐Rogers Functions for Arbitrary Pairs of Graphs
Random Structures &Algorithms, Volume 68, Issue 3, May 2026.ABSTRACT Let fF,G(n)$$ {f}_{F,G}(n) $$ be the largest size of an induced F$$ F $$‐free subgraph that every n$$ n $$‐vertex G$$ G $$‐free graph is guaranteed to contain. We prove that for any triangle‐free graph F$$ F $$, fF,K3(n)=fK2,K3(n)1+o(1)=n12+o(1).$$ {f}_{F,{K}_3}(n)={f}_{K_2,{K}_3}{(n)}^{1+o(1)}={n}^{\frac{1}{2}+o(1)}. $$Along the way we give a
Dhruv Mubayi, Jacques Verstraëte
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Color-critical graphs and hypergraphs
Journal of Combinatorial Theory, Series B, 1974 Abstract The main purpose of this paper is to present a technique for obtaining constructions of color-critical graphs. The technique consists in reducing color-critical hypergraphs to color-critical graphs, and the constructions obtained generalize and unify known constructions.
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The dynamics of criminal collaboration: Multiplex ties in mafia networks
Criminology, Volume 64, Issue 2, Page 284-312, May 2026.Abstract This study examines how social embeddedness and multiplex relationships shape criminal collaboration within organized crime networks. Drawing on data from three major investigations into the ‘Ndrangheta, we analyze how kinship, clan affiliation, leadership, and prior interactions influence participation in meetings and phone calls.
Francesco Calderoni +2 more
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Fractional clique decompositions of dense hypergraphs
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract In 2014, Keevash famously proved the existence of (n,q,r)$(n,q,r)$‐Steiner systems as part of settling the Existence Conjecture of Combinatorial Designs (dating from the mid‐1800s). In 2020, Glock, Kühn, and Osthus conjectured a minimum degree generalization: specifically that minimum (r−1)$(r-1)$‐degree at least (1−Cqr−1)n$(1-\frac{C}{q^{r-1}}
Michelle Delcourt +2 more
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Color-bounded hypergraphs, V: host graphs and subdivisions
Discussiones Mathematicae Graph Theory, 2011 A color-bounded hypergraph is a hypergraph (set system) with ver- tex set X and edge set e = {E1, . . . ,Em}, together with integers si and ti satisfying 1 ≤ si ≤ ti ≤ |E1| for each i = 1, . . . ,m. A vertex coloring φ is proper if for every i, the number of colors occurring in edge 1 satisfies si ≤ |φ(Ei)| ≤ t i.
Csilla Bujtás +2 more
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A Vulnerability Lens for Intuitive‐Logic Scenarios
FUTURES &FORESIGHT SCIENCE, Volume 8, Issue 1, April 2026.ABSTRACT Exploration of possibilities by means of intuitive logic is hampered by a large number of scenarios, which easily exceed the limits imposed by human bounded rationality. While many practitioners constrain their scenarios within a 2 × 2 $2\times 2$ matrix by design, more structured approaches point to rationales such as eliminating ...
Guido Fioretti
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