Results 41 to 50 of about 9,106,907 (129)
Packing Chromatic Number of Circular Fans and Mesh of Trees
International Journal of Mathematics and Soft Computing, 2014 The packing chromatic number $\raisebox{2pt}{$\chi$}_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi:V(G)\longrightarrow \{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$.
Indra Rajasingh, S. Roy, Albert William
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The packing chromatic number of the square lattice is at least 12
CoRR, 2010 The packing chromatic number $χ_ρ(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set $V(G)$ can be partitioned into disjoint classes $X_1, ..., X_k$, where vertices in $X_i$ have pairwise distance greater than $i$. For the 2-dimensional square lattice $\mathbb{Z}^2$ it is proved that $χ_ρ(\mathbb{Z}^2) \geq 12$, which improves the ...
Jan Ekstein +3 more
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Packing Chromatic Number of Coronae of Paths and Cycles [PDF]
, 2019 Pakirno kromatično število $chi_{pi}(G)$ grafa $G$ je najmanjši $k$, za katerega lahko poiščemo $k$-pakirno barvanje grafa, torej najmanjši $k$, za katerega obstaja taka funkcija $pi: (G) to [k]$, da iz $pi(u) = pi(v)$ sledi, da je razdalja med $u$ in $v$
Robba, Barbara
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On the Packing Chromatic Number of Trees, Cartesian Products and Some Infinite Graphs
Electronic Notes in Discrete Mathematics, 2008 Abstract A subset A of vertices in a graph G is an r-packing if the distance between every pair of distinct vertices in A is more than r. The packing chromatic number, χ ρ ( G ) , is the smallest k for which there exists some partition V 1 , V 2 , … , V k of the vertex set of G such that V r is an r-packing ...
Douglas F. Rall +3 more
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Hardness of approximation for orthogonal rectangle packing and covering problems [PDF]
, 2009 Bansal and Sviridenko [N. Bansal, M. Sviridenko, New approximability and inapproximability results for 2-dimensional bin packing, in: Proceedings of the 15th Annual ACM–SIAM Symposium on Discrete Algorithms, SODA, 2004, pp.
Chlebikova, Janka +3 more
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Packing coloring of graphs [PDF]
, 2022 Pakirno barvanje grafe je dobro barvanje vozlišč, pri katerem sta poljubni dve vozlišči z isto barvo i na razdalji večji kot i. Pakirno kromatično število je najmanjše število barv, ki jih potrebujemo za tako barvanje grafa.
Ličina, Tomaž
core
High-speed chromatic dispersion monitoring of a two-channel WDM system using a single TPA microcavity [PDF]
, 2008 Chromatic dispersion monitoring of two 160 Gb/s wavelength channels using a TPA Microcavity is presented. As the microcavity exhibits a wavelength resonance characteristic, a single device could monitor a number of different WDM-channels ...
Guo, Wei Hua +7 more
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S-packing chromatic critical graphs [PDF]
For a non-decreasing sequence of positive integers $S=(s_1,s_2,ldots)$, the $S$-packing chromatic number of a graph $G$ is denoted by $chi_S(G)$. In this paper, $chi_S$-critical graphs are introduced as the graphs $G$ such that $chi_S(H) < chi_S(G)$ for ...
Gozüpek, Didem +3 more
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Packing chromatic number, $(1,1,2,2)$-colorings, and characterizing the Petersen graph
, 2016 16 pages, 4 ...
Brešar, Boštjan +3 more
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On Sierpiński packing chromatic number and recognition of Sierpiński products
The Sierpiński product $G \otimes _f H$ of graphs $G$ and $H$ with respect to a function $f \colon V(G)\rightarrow V(H)$ has the vertex set $V(G)\times V(H)$. For every $g\in V(G)$ it contains a disjoint copy $gH$ of $H$, and for every edge $gg'$ of $G$ there is the edge $(g,f(g'))(g',f(g))$ between $gH$ and $g'H$. In this paper, the Sierpiński packing
Holub, Přemysl, Klavžar, Sandi
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