Results 31 to 40 of about 117,877 (279)
Chromatic number via Turán number
Discrete Mathematics, 2017 A Kneser representation KG(H) for a graph G is a bijective assignment of hyperedges of a hypergraph H to the vertices of G such that two vertices of G are adjacent if and only if the corresponding hyperedges are disjoint. In this paper, we introduce a colored version of the Turan number and use that to determine the chromatic number of some families of
Meysam Alishahi, Hossein Hajiabolhassan
openaire +2 more sources
Total dominator chromatic number of a graph [PDF]
Transactions on Combinatorics, 2015 Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes.
Adel P. Kazemi
doaj
Unified Spectral Bounds on the Chromatic Number
Discussiones Mathematicae Graph Theory, 2015 One of the best known results in spectral graph theory is the following lower bound on the chromatic number due to Alan Hoffman, where μ1 and μn are respectively the maximum and minimum eigenvalues of the adjacency matrix: χ ≥ 1+μ1/−μn.
Elphick Clive, Wocjan Pawel
doaj +1 more source
ON LOCAL ANTIMAGIC CHROMATIC NUMBER OF GRAPHS [PDF]
Journal of Algebraic Systems, 2020 A {it local antimagic labeling} of a connected graph $G$ with at least three vertices, is a bijection $f:E(G) rightarrow {1,2,ldots , |E(G)|}$ such that for any two adjacent vertices $u$ and $v$ of $G$, the condition $omega _{f}(u) neq omega _{f}(v ...
S. Shaebani
doaj +1 more source
Weighted graphs: Eigenvalues and chromatic number
Electronic Journal of Graph Theory and Applications, 2016 We revisit Hoffman relation involving chromatic number $\chi$ and eigenvalues. We construct some graphs and weighted graphs such that the largest and smallest eigenvalues $\lambda$ dan $\mu$ satisfy $\lambda=(1-\chi)\mu.$ We study in particular the ...
Charles Delorme
doaj +1 more source
Colouring the Triangles Determined by a Point Set [PDF]
, 2011 Let P be a set of n points in general position in the plane. We study the chromatic number of the intersection graph of the open triangles determined by P.
Fabila-Monroy, Ruy, Wood, David R.
core +4 more sources
A Tight Bound on the Set Chromatic Number
Discussiones Mathematicae Graph Theory, 2013 We provide a tight bound on the set chromatic number of a graph in terms of its chromatic number. Namely, for all graphs G, we show that χs(G) > ⌈log2 χ(G)⌉ + 1, where χs(G) and χ(G) are the set chromatic number and the chromatic number of G ...
Sereni Jean-Sébastien +1 more
doaj +1 more source
Locally identifying coloring in bounded expansion classes of graphs [PDF]
, 2012 A proper vertex coloring of a graph is said to be locally identifying if the sets of colors in the closed neighborhood of any two adjacent non-twin vertices are distinct.
Gonçalves, Daniel +2 more
core +7 more sources
The b-chromatic number of power graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x i adjacent to a
Brice Effantin, Hamamache Kheddouci
doaj +2 more sources
Trees with Certain Locating-chromatic Number
Journal of Mathematical and Fundamental Sciences, 2016 The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are ...
Dian Kastika Syofyan +2 more
doaj +1 more source