Results 31 to 40 of about 8,753,370 (220)
The fractional chromatic number of triangle-free subcubic graphs [PDF]
, 2014 Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14 / 5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free ...
Král’, Daniel +5 more
core +1 more source
The harmonious chromatic number of almost all trees [PDF]
, 1995 A harmonious colouring of a simple graph G is a proper vertex colouring such that each pair of colours appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colours in such a colouring.For any positive integer ...
Edwards, Keith
core +1 more source
PACKING CHROMATIC NUMBER OF CERTAIN GRAPHS [PDF]
International Journal of Pure and Apllied Mathematics, 2013 The packing chromatic number (G) of a graph G is the smallest integer k for which there exists a mapping : V (G) −→ {1,2,...,k} such that any two vertices of color i are at distance at least i + 1. It is a frequency assignment problem used in wireless networks, which is also called broadcasting coloring.
A. William, S. Roy
openaire +1 more source
Packing Coloring of Some Undirected and Oriented Coronae Graphs
Discussiones Mathematicae Graph Theory, 2017 The packing chromatic number χρ(G) of a graph G is the smallest integer k such that its set of vertices V(G) can be partitioned into k disjoint subsets V1, . . . , Vk, in such a way that every two distinct vertices in Vi are at distance greater than i in
Laïche Daouya +2 more
doaj +1 more source
On the packing chromatic number of square and hexagonal lattice
Ars Mathematica Contemporanea, 2013 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 , with the condition that vertices in X i have pairwise distance greater than i . We show that the packing chromatic number for the hexagonal lattice ℋ
Korže, Danilo, Vesel, Aleksander
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The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs [PDF]
Journal of Ultra Scientist of Physical Sciences Section A, 2021 The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,...,Vk , where vertices in Vi have pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}
B. CHALUVARAJU, M. KUMARA
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On packing chromatic number of subcubic outerplanar graphs
CoRR, 2017 Although it has recently been proved that the packing chromatic number is unbounded on the class of subcubic graphs, there exists subclasses in which the packing chromatic number is finite (and small). These subclasses include subcubic trees, base-3 Sierpi{ń}ski graphs and hexagonal lattices.In this paper we are interested in the packing chromatic ...
Gastineau, Nicolas +2 more
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Bioinspired Adaptive Sensors: A Review on Current Developments in Theory and Application
Advanced Materials, EarlyView.This review comprehensively summarizes the recent progress in the design and fabrication of sensory‐adaptation‐inspired devices and highlights their valuable applications in electronic skin, wearable electronics, and machine vision. The existing challenges and future directions are addressed in aspects such as device performance optimization ...
Guodong Gong +12 more
wiley +1 more source
The Packing Chromatic Number of the Infinite Square Grid is 15
, 2023 Abstract A packing k -coloring is a natural variation on the standard notion of graph k -coloring, where vertices are assigned numbers from $$\{1, \ldots , k\}$$
Bernardo Subercaseaux +1 more
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The Packing Chromatic Number of the Infinite Square Grid is At Least 14
, 2022 Code corresponding to the paper "The Packing Chromatic Number of the Infinite Square Grid is At Least 14", accepted at SAT'2022. A README file explains how to use it.
Subercaseaux, Bernardo +1 more
openaire +5 more sources