Results 31 to 40 of about 11,451 (248)
On equitable coloring of corona of wheels
Electronic Journal of Graph Theory and Applications, 2016 The notion of equitable colorability was introduced by Meyer in $1973$ \cite{meyer}. In this paper we obtain interesting results regarding the equitable chromatic number $\chi_{=}$ for the corona graph of a simple graph with a wheel graph $G\circ W_n ...
J. Vernold Vivin, K. Kaliraj
doaj +1 more source
Universal Sets for Straight-Line Embeddings of Bicolored Graphs
, 2011 A set S of n points is 2-color universal for a graph G on n vertices if for every proper 2-coloring of G and for every 2-coloring of S with the same sizes of color classes as G has, G is straight-line embeddable on S.
Cibulka, Josef +4 more
core +1 more source
On $r$-Equitable Coloring of Complete Multipartite Graphs
, 2013 Let $r \geqslant 0$ and $k \geqslant 1$ be integers. We say that a graph $G$ has an $r$-equitable $k$-coloring if there exists a proper $k$-coloring of $G$ such that the sizes of any two color classes differ by at most $r$.
Yen, Chih-Hung
core +1 more source
Equitable Coloring and the Maximum Degree
European Journal of Combinatorics, 1994 The equitable \(h\)-coloring conjecture says that a connected graph \(G\) is equitable \(h(G)\)-colorable if it is different from \(K_ n\), \(C_{2n+1}\) and \(K_{2n+1,2n+1}\) for all \(n\geq 1\). This conjecture is proved for graphs \(G\) with \(h(G)\geq | G|/2\) or \(h(G)\leq 3\), where \(h(G)\) is the maximum vertex degree of \(G\).
Chen, Bor-Liang +2 more
openaire +1 more source
Perfect 3-colorings of the cubic graphs of order 10
Electronic Journal of Graph Theory and Applications, 2017 Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect m-coloring of a graph G with m colors is a partition of the vertex set of G into m parts A_1, A_2, ..., A_m such that, for all $ i,j \in \lbrace ...
Mehdi Alaeiyan, Ayoob Mehrabani
doaj +1 more source
Perfect 2-colorings of the cubic graphs of order less than or equal to 10
AKCE International Journal of Graphs and Combinatorics, 2020 Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect -coloring of a graph with colors is a partition of the vertex set of into m parts , . . .
Mehdi Alaeiyan, Ayoob Mehrabani
doaj +1 more source
Structural Parameterizations for Equitable Coloring [PDF]
, 2020 An $n$-vertex graph is equitably $k$-colorable if there is a proper coloring of its vertices such that each color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k \right\rceil$ times. While classic Vertex Coloring is fixed parameter tractable under well established parameters such as pathwidth and feedback vertex set, Equitable ...
Guilherme C. M. Gomes +2 more
openaire +2 more sources
On the binary codes with parameters of triply-shortened 1-perfect codes
, 2011 We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary $(n=2^m-3, 2^{n-m-1}, 4)$ code $C$, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of an equitable ...
D.S. Krotov +7 more
core +1 more source
Mapping the evolution of mitochondrial complex I through structural variation
FEBS Letters, EarlyView.Respiratory complex I (CI) is crucial for bioenergetic metabolism in many prokaryotes and eukaryotes. It is composed of a conserved set of core subunits and additional accessory subunits that vary depending on the organism. Here, we categorize CI subunits from available structures to map the evolution of CI across eukaryotes. Respiratory complex I (CI)
Dong‐Woo Shin +2 more
wiley +1 more source
Equitable coloring of random graphs [PDF]
Random Structures & Algorithms, 2009 AbstractAn equitable coloring of a graph is a proper vertex coloring such that the sizes of any two color classes differ by at most one. The least positive integer k for which there exists an equitable coloring of a graph G with k colors is said to be the equitable chromatic number of G and is denoted by χ=(G).
Krivelevich, Michael, Patkós, Balázs
openaire +1 more source