Results 71 to 80 of about 8,657,296 (197)
Bounds on the Distinguishing Chromatic Number [PDF]
The Electronic Journal of Combinatorics, 2009 Collins and Trenk define the distinguishing chromatic number $\chi_D(G)$ of a graph $G$ to be the minimum number of colors needed to properly color the vertices of $G$ so that the only automorphism of $G$ that preserves colors is the identity. They prove results about $\chi_D(G)$ based on the underlying graph $G$.
Karen L. Collins +2 more
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On the difference between chromatic number and dynamic chromatic number of graphs
Discrete Mathematics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arash Ahadi +3 more
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The Local Chromatic Number [PDF]
, 2013 The local chromatic number ψ(G) of a graph G is a graph colouring parameter that is defined as ψ(G) = min c max v∈V (G) |c(Γ̄(v))| where the minimum is taken over all proper colourings c of G and Γ̄(v) denotes the closed neighbourhood of a vertex v.
Osang, Georg Fritz, Georg Osang
core
The fractional chromatic number of the plane [PDF]
Combinatorica, 2016 20 pages, 10 ...
Daniel W. Cranston, Landon Rabern
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The $b$-Chromatic Number and $f$-Chromatic Vertex Number of Regular Graphs
Discret. Appl. Math., 2013 The $b$-chromatic number of a graph $G$, denoted by $b(G)$, is the largest positive integer $k$ such that there exists a proper coloring for G with $k$ colors in which every color class contains at least one vertex adjacent to some vertex in each of the other color classes, such a vertex is called a dominant vertex. The $f$-chromatic vertex number of a
El-Sahili, Amine +3 more
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On the complexity of the circular chromatic number [PDF]
Journal of Graph Theory, 2004 AbstractCircular chromatic number, χcis a natural generalization of chromatic number. It is known that it isNP‐hard to determine whether or not an arbitrary graphGsatisfies χ(G)=χc(G). In this paper we prove that this problem isNP‐hard even if the chromatic number of the graph is known. This answers a question of Xuding Zhu.
Hamed Hatami, Ruzbeh Tusserkani
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Face-wise Chromatic Number [PDF]
, 2016 The chromatic number is a well-studied graph invariant. This is the smallest number of colors necessary to color all the vertices such that no two vertices adjacent to the same edge are the same color.
Myrant, Cat
core +1 more source
Chromatic and clique numbers of a class of perfect graphs [PDF]
Transactions on Combinatorics, 2015 Let p be a prime number and n be a positive integer. The graph G p (n) is a graph with vertex set [n]=1,2,ldots,n , in which there is an arc from u to v if and only if uneqv and pnmidu+v . In this paper it is shown that G p (n) is a perfect
Mohammad Reza Fander
doaj
On the adaptable chromatic number of graphs [PDF]
, 2008 The adaptable chromatic number of a graph G is the smallest integer k such that for any edge k-colouring of G there exists a vertex k-colouring of G in which the same colour never appears on an edge and both its endpoints.
Hell, Pavol, Zhu, Xuding
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The Incidence Chromatic Number of Toroidal Grids
Discussiones Mathematicae Graph Theory, 2013 An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f, or the edge vw equals e or f.
Sopena Éric, Wu Jiaojiao
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