Results 21 to 30 of about 142 (135)
On Hypergraph and Graph Isomorphism with Bounded Color Classes [PDF]
, 2006 Using logspace counting classes we study the computational complexity of hypergraph and graph isomorphism where the vertex sets have bounded color classes for certain specific bounds. We also give a polynomial-time algorithm for hypergraph isomorphism for bounded color classes of arbitrary size.
Vikraman Arvind, Johannes Köbler
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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
+5 more sources
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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Density Conditions for k $k$ Vertex‐Disjoint Triangles in Tripartite Graphs
Journal of Graph Theory, EarlyView.ABSTRACT Let n , k $n,k$ be positive integers such that n ≥ k $n\ge k$ and G $G$ be a tripartite graph with parts A , B , C $A,B,C$ such that ∣ A ∣ = ∣ B ∣ = ∣ C ∣ = n $| A| =| B| =| C| =n$. Denote the edge densities of G [ A , B ] , G [ A , C ] $G[A,B],G[A,C]$ and G [ B , C ] $G[B,C]$ by α , β $\alpha ,\beta $ and γ $\gamma $, respectively.
Mingyang Guo, Klas Markström
wiley +1 more source
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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Chromatic Ramsey Numbers and Two‐Color Turán Densities
Journal of Graph Theory, EarlyView.ABSTRACT Given a graph G, its 2‐color Turán number ex ( 2 ) ( n , G ) is the maximum number of edges in an n‐vertex graph, such that the edges can be colored with two colors avoiding a monochromatic copy of G. Let π ( 2 ) ( G ) = lim n → ∞ ex ( 2 ) ( n , G ) / n 2 be the 2‐color Turán density of G.
Maria Axenovich, Simon Gaa, Dingyuan Liu
wiley +1 more source
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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CAAI Transactions on Intelligence Technology, EarlyView.ABSTRACT Cognitive diagnosis aims to infer learners' knowledge states from their exercise responses, enabling personalised education at scale. Existing methods represent exercises solely by coarse‐grained knowledge component annotations, overlooking semantic content and step‐level cognitive processes.
Youheng Bai +4 more
wiley +1 more source
Clusterix: A Hybrid Visualization Model for Hierarchically Clustered Networks
Computer Graphics Forum, EarlyView.Abstract We introduce Clusterix, a novel hybrid visualization model for representing hierarchically clustered networks, which also supports directed and weighted edges. Clusterix offers an integrated view of both the network and its full cluster hierarchy by compactly visualizing the cluster inclusion tree enriched with links of the network.
Carla Binucci +6 more
wiley +1 more source
Orientations of Graphs With at Most One Directed Path Between Every Pair of Vertices
Journal of Graph Theory, Volume 113, Issue 1, Page 143-164, September 2026.ABSTRACT Given a graph G, we say that an orientation D of G is a KT orientation if, for all u , v ∈ V ( D ), there is at most one directed path (in any direction) between u and v. Graphs that admit such orientations have been used to construct graphs with large chromatic number and small clique number that served as counterexamples to various ...
Barbora Dohnalová +3 more
wiley +1 more source