Results 41 to 50 of about 1,425,497 (376)
Brief Announcement: Streaming and Massively Parallel Algorithms for Edge Coloring [PDF]
, 2019 A valid edge-coloring of a graph is an assignment of "colors" to its edges such that no two incident edges receive the same color. The goal is to find a proper coloring that uses few colors.
Behnezhad, Soheil +4 more
core +1 more source
Tight Bounds for Online Edge Coloring [PDF]
IEEE Annual Symposium on Foundations of Computer Science, 2019 Vizing's celebrated theorem asserts that any graph of maximum degree Δ admits an edge coloring using at most Δ+1 colors. In contrast, Bar-Noy, Motwani and Naor showed over a quarter century ago that the trivial greedy algorithm, which uses 2Δ-1 colors ...
I. Cohen, Binghui Peng, David Wajc
semanticscholar +1 more source
On edge-colored saturation problems [PDF]
Journal of Combinatorics, 2020 Let $\mathcal{C}$ be a family of edge-colored graphs. A $t$-edge colored graph $G$ is $(\mathcal{C}, t)$-saturated if $G$ does not contain any graph in $\mathcal{C}$ but the addition of any edge in any color in $[t]$ creates a copy of some graph in $\mathcal{C}$. Similarly to classical saturation functions, define $\mathrm{sat}_t(n, \mathcal{C})$ to be
Michael Tait +8 more
openaire +3 more sources
Placement Delivery Array Design Through Strong Edge Coloring of Bipartite Graphs [PDF]
IEEE Communications Letters, 2016 The technique of coded caching proposed by Madddah-Ali and Niesen is a promising approach to alleviate the load of networks during peak-traffic times. Recently, placement delivery array (PDA) was presented to characterize both the placement and delivery ...
Qifa Yan +3 more
semanticscholar +1 more source
Edge-Coloring Bipartite Graphs [PDF]
Journal of Algorithms, 2000 This note provides an algorithm for finding \(\Delta\)(colors)-edge-coloring of a bipartite graph of order \(n\) and size \(m\) in time \(T+O(m\log \Delta)\) where \(T\) is the time needed to find a perfect matching in a \(k\)-regular bipartite graph, \(k\leq \Delta\), and \(\Delta\) is the maximum degree of vertices.
A. Kapoor, Rizzi, Romeo
openaire +4 more sources
Facial graceful coloring of plane graphs [PDF]
Opuscula MathematicaLet \(G\) be a plane graph. Two edges of \(G\) are facially adjacent if they are consecutive on the boundary walk of a face of \(G\). A facial edge coloring of \(G\) is an edge coloring such that any two facially adjacent edges receive different colors ...
Július Czap
doaj +1 more source
The 1-2-3 Conjecture for Hypergraphs [PDF]
, 2016 A weighting of the edges of a hypergraph is called vertex-coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e., every edge contains at least two vertices with different weighted degrees.
Kalkowski, Maciej +2 more
core +2 more sources
Degenerate matchings and edge colorings [PDF]
Discrete Applied Mathematics, 2018 A matching $M$ in a graph $G$ is $r$-degenerate if the subgraph of $G$ induced by the set of vertices incident with an edge in $M$ is $r$-degenerate. Goddard, Hedetniemi, Hedetniemi, and Laskar (Generalized subgraph-restricted matchings in graphs, Discrete Mathematics 293 (2005) 129-138) introduced the notion of acyclic matchings, which coincide with ...
Julien Baste +2 more
openaire +3 more sources
A polyhedral approach to edge coloring [PDF]
Operations Research Letters, 1991 The edge coloring problem is formulated as an integer linear program of covering edges by matchings. For the NP-hard case of 3-regular graphs a linear programming relaxation with additional constraints is considered using column generation. The theory and the algorithm use the fact that the chromatic index is equal to 3 or 4.
NEMHAUSER, GL, PARK, S Park, Sungsoo
openaire +4 more sources
A structural approach to the graceful coloring of a subclass of trees
Heliyon, 2023 Let M={1,2,..m} and G be a simple graph. A graceful m-coloring of G is a proper vertex coloring of G using the colors in M which leads to a proper edge coloring using M∖{m} colors such that the associated color of each edge is the absolute difference ...
Laavanya D, Devi Yamini S
doaj +1 more source