Results 211 to 220 of about 11,451 (248)
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Equitable Colorings of Hypergraphs with r Colors
Journal of Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akhmejanova, M., Shabanov, D. A.
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Equitable coloring of hypergraphs
Discrete Applied Mathematics, 2019A hypergraph is equitably k-colorable if its vertices can be partitioned into k sets/color classes in such a way that monochromatic edges are avoided and the number of vertices in any two color classes differs by at most one. We prove that the problem of equitable 2-coloring of hypergraphs is NP-complete even for 3-uniform hyperstars. Finally, we apply
Hanna Furmańczyk, Paweł Obszarski
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Journal of Graph Theory, 2023
AbstractIn this paper, we consider equitable oriented colorings of graphs. Such coloring is a natural combination of two well‐known colorings: oriented coloring and equitable coloring. An oriented ‐coloring of an oriented graph is an arc‐preserving homomorphism from into an oriented graph on vertices, or colors.
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AbstractIn this paper, we consider equitable oriented colorings of graphs. Such coloring is a natural combination of two well‐known colorings: oriented coloring and equitable coloring. An oriented ‐coloring of an oriented graph is an arc‐preserving homomorphism from into an oriented graph on vertices, or colors.
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Equitably Colored Balanced Incomplete Block Designs
Journal of Combinatorial Designs, 2015AbstractIn this paper, we determine the necessary and sufficient conditions for the existence of an equitably ℓ‐colorable balanced incomplete block design for any positive integer. In particular, we present a method for constructing nontrivial equitably ℓ‐colorable BIBDs and prove that these examples are the only nontrivial examples that exist. We also
Luther, Robert D., Pike, David A.
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On Equitable Colorings of Hypergraphs
Mathematical Notes, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A QUESTION ON RELAXED EQUITABLE COLORING
Discrete Mathematics, Algorithms and Applications, 2012An equitable (k, d)-coloring is a (k, d)-coloring that is also equitable. In this paper, we raise a conjecture that if G is a graph such that for each edge xy ∈ E(G), the sum d(x) + d(y) at most 2r + 1, then G has a d-relaxed equitable coloring with r + 1 - d colors. We prove that if graph G meet d(x) + d(y) ≤ 2r for every edge xy ∈ E(G) and |G| = rs,
Gao, Wei, Zhou, Fen
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On Equitable Colorings of Sparse Graphs
Bulletin of the Malaysian Mathematical Sciences Society, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On equitable near proper coloring of graphs
2022Summary: A defective vertex coloring of a graph is a coloring in which some adjacent vertices may have the same color. An edge whose adjacent vertices have the same color is called a bad edge. A defective coloring of a graph \(G\) with minimum possible number of bad edges in \(G\) is known as a near proper coloring of \(G\). In this paper, we introduce
Jose, Sabitha +2 more
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Equitable versus nearly equitable coloring and the Chen-Lih-Wu conjecture
Combinatorica, 2010A proper vertex colouring of a graph is called equitable if the colour classes differ in size by at most one. The authors extend the conjecture of \textit{B.-L. Chen}, \textit{K.-W. Lih}, and \textit{P.-L. Wu} [Eur. J. Comb. 15, No. ~5, 443--447 (1994; Zbl 0809.05050)] to disconnected graphs.
Kierstead, Henry A. +1 more
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