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Notes on complexity of packing coloring [PDF]
Information Processing Letters, 2017 A packing $k$-coloring for some integer $k$ of a graph $G=(V,E)$ is a mapping $ :V\to\{1,\ldots,k\}$ such that any two vertices $u, v$ of color $ (u)= (v)$ are in distance at least $ (u)+1$. This concept is motivated by frequency assignment problems. The \emph{packing chromatic number} of $G$ is the smallest $k$ such that there exists a packing $k$-
Minki Kim +3 more
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Independence Number and Packing Coloring of Generalized Mycielski Graphs
Discussiones Mathematicae Graph Theory, 2021 For a positive integer k ⩾ 1, a graph G with vertex set V is said to be k-packing colorable if there exists a mapping f : V ↦ {1, 2, . . ., k} such that any two distinct vertices x and y with the same color f(x) = f(y) are at distance at least f(x) + 1 ...
Bidine Ez Zobair +2 more
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On distance dominator packing coloring in graphs
Discussiones Mathematicae Graph Theory, 2021 Let G be a graph and let S = (s1,s2,..., sk) be a non-decreasing sequence of positive integers. An S-packing coloring of G is a mapping c : V(G) ? {1, 2,..., k} with the following property: if c(u) = c(v) = i, then d(u,v) > si for any i ? {1, 2,...,k}.
Jasmina Ferme, Dasa Stesl
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Packing Coloring of Some Undirected and Oriented Coronae Graphs [PDF]
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
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Packing coloring of generalized Sierpinski graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $c$ such that the vertex set $V(G)$ can be partitioned into sets $X_1, . . .
Danilo Korze, Aleksander Vesel
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Counting packings of list-colorings of graphs [PDF]
Enumerative Combinatorics and Applications11 ...
Hemanshu Kaul, Jeffrey A. Mudrock
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Random Structures & Algorithms, 2023 AbstractList coloring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list‐coloring, we seek many in parallel. Our explorations have uncovered a potentially rich seam of interesting problems spanning chromatic graph theory. Given a ‐list‐assignment of a graph ,
Stijn Cambie +3 more
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Further results and questions on S-packing coloring of subcubic graphs [PDF]
Discrete MathematicsFor non-decreasing sequence of integers $S=(a_1,a_2, \dots, a_k)$, an $S$-packing coloring of $G$ is a partition of $V(G)$ into $k$ subsets $V_1,V_2,\dots,V_k$ such that the distance between any two distinct vertices $x,y \in V_i$ is at least $a_{i}+1$, $
Maidoun Mortada, Olivier Togni
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Packing coloring of Sierpiński-type graphs [PDF]
Aequationes mathematicae, 2017 26 pages, 16 ...
B. Brešar, Jasmina Ferme
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On S-packing edge-coloring of graphs with given edge weight
Discussiones Mathematicae Graph TheoryJian Lu, Xiang-Feng Pan
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