Results 31 to 40 of about 135,434 (260)
On multiset colorings of generalized corona graphs [PDF]
Mathematica Bohemica, 2016 A vertex $k$-coloring of a graph $G$ is a \emph{multiset $k$-coloring} if $M(u)\neq M(v)$ for every edge $uv\in E(G)$, where $M(u)$ and $M(v)$ denote the multisets of colors of the neighbors of $u$ and $v$, respectively. The minimum $k$ for which $G$ has
Yun Feng, Wensong Lin
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Distinguishing homomorphisms of infinite graphs [PDF]
, 2012 We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper $n$-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph $
Bonato, Anthony, Delic, Dejan
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Approximate and Exact Results for the Harmonious Chromatic Number [PDF]
Discussiones Mathematicae Graph Theory, 2021 Graph coloring is a fundamental topic in graph theory that requires an assignment of labels (or colors) to vertices or edges subject to various constraints.
Ruxandra Marinescu-Ghemeci +2 more
semanticscholar +1 more source
On the complexity of deciding whether the distinguishing chromatic number of a graph is at most two [PDF]
Discrete Mathematics, 2009 In an article Cheng (2009) [3] published recently in this journal, it was shown that when k>=3, the problem of deciding whether the distinguishing chromatic number of a graph is at most k is NP-hard. We consider the problem when k=2.
Elaine M. Eschen +3 more
semanticscholar +1 more source
An Evaluation of a Battery of Functional and Structural Tests as Predictors of Likely Risk of Progression of Age-Related Macular Degeneration. [PDF]
, 2018 Purpose: To evaluate the ability of visual function and structural tests to identify the likely risk of progression from early/intermediate to advanced AMD, using the Age-Related Eye Disease Study (AREDS) simplified scale as a surrogate for risk of ...
Bailey, C. +3 more
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Distinguishing chromatic number of Hamiltonian circulant graphs
, 2023 The distinguishing chromatic number of a graph $G$ is the smallest number of colors needed to properly color the vertices of $G$ so that the trivial automorphism is the only symmetry of $G$ that preserves the coloring. We investigate the distinguishing chromatic number for Hamiltonian circulant graphs with maximum degree at most 4.
Barrus, Michael D. +2 more
openaire +2 more sources
A New Game Invariant of Graphs: the Game Distinguishing Number [PDF]
, 2017 The distinguishing number of a graph $G$ is a symmetry related graph invariant whose study started two decades ago. The distinguishing number $D(G)$ is the least integer $d$ such that $G$ has a $d$-distinguishing coloring.
Gravier, Sylvain +3 more
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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
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On the total and AVD-total coloring of graphs
AKCE International Journal of Graphs and Combinatorics, 2020 A total coloring of a graph G is an assignment of colors to the vertices and the edges such that (i) no two adjacent vertices receive same color, (ii) no two adjacent edges receive same color, and (iii) if an edge e is incident on a vertex v, then v and ...
B. S. Panda, Shaily Verma, Yash Keerti
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Order Quasisymmetric Functions Distinguish Rooted Trees [PDF]
, 2017 Richard P. Stanley conjectured that finite trees can be distinguished by their chromatic symmetric functions. In this paper, we prove an analogous statement for posets: Finite rooted trees can be distinguished by their order quasisymmetric functions ...
Hasebe, Takahiro, Tsujie, Shuhei
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