Strong coloring - Wikipedia
In graph theory, a strong coloring, with respect to a partition of the vertices into (disjoint) subsets of equal sizes, is a (proper) vertex coloring in which every color appears exactly once in every part. A graph is strongly k-colorable if, for each partition of the vertices into sets of size k, it …
A strong vertex coloring of a hypergraph assigns distinct col-ors to vertices that are contained in a common hyperedge. This captures many previously studied graph coloring problems. We present nearly tight upper and lower bound on approximating general hypergraphs, both …
A strong edge-coloring is a proper edge-coloring, with the further condition that no two edges with the same color lie on a path of length three. The strong edge chromatic number is the minimum number of colors that allow a strong edge-coloring.
On strong edge-coloring of graphs with maximum degree 5
2024年2月15日 · A strong k-edge-coloring of a graph G is a mapping φ from E (G) to {1, 2, …, k} such that φ (e 1) ≠ φ (e 2) for any d G (e 1, e 2) ≤ 2. The strong chromatic index of G, denoted by χ s ′ (G), is the smallest integer k such that G admits a strong k-edge-coloring. Strong edge-coloring was first introduced by Fouquet and Jolivet [9]. In ...
Graph Entropy Based on Strong Coloring of Uniform Hypergraphs …
2021年12月22日 · In this paper, we determine the extremal values for graph entropy based on strong coloring for k-uniform hypergraph H. For k-uniform hypergraph H (k ≥ c (H) + 2) with n vertices and m edges, when n − m + 1 − c (H) k − 1 is an integer and m ≤ (2 − c (H)) k + (k − 1) 2 − c (H), we obtain an upper bound of the graph entropy based ...
strong coloring is a one-to-one mapping, which imposes χs(H) = n. In view of Remark 1.10, we only consider strong coloring in the case of l = 1 and use a shorthand notation Π r
List Strong Edge-Colorings of Sparse Graphs - Springer
2023年10月17日 · A strong edge-coloring of a graph $$G=(V,E)$$ is a partition of its edge set E into induced matchings. In this paper, we will study the list version of strong edge-colorings of several classes of sparse graphs, including bipartite graphs and graphs with small edge weight, where the edge weight of a graph is defined by $$\max \{ d_G(u) + d_G(v ...
Strong edge-colorings of sparse graphs with large maximum degree
2016年10月18日 · Strong edge-colorings of sparse graphs with large maximum degree. A {\em strong -edge-coloring} of a graph is a mapping from to such that every two adjacent edges or two edges adjacent to the same edge receive distinct colors. The {\em strong chromatic index} of a graph is the smallest integer such that admits a strong -edge-coloring.
Strong Colorings of Hypergraphs - SpringerLink
A strong vertex coloring of a hypergraph assigns distinct colors to vertices that are contained in a common hyperedge. This captures many previously studied graph coloring problems. We present nearly tight upper and lower bound on approximating general hypergraphs, both …
Strong coloring 2‐regular graphs: Cycle restrictions and partial ...
2022年1月28日 · Strong coloring 2-regular graphs: Cycle restrictions and partial colorings. Jessica McDonald, Gregory J. Puleo. First published: 28 January 2022. https://doi.org/10.1002/jgt.22800. Read the full text. PDF. Tools. Share. Abstract. Let be a graph with , and let be obtained from by gluing in vertex-disjoint copies of .