Planar graphlist 2-distance coloringcyclesmaximum degreeA 2-distance coloring of G is a function φ: V (G) →{1, 2,…,k}, such that for every two distinct vertices u, v in G, φ(u)≠φ(v) if 0 < dG(u,v) ≤ 2. The 2-distance chromatic number of G is the least integer ...
For graphs of bounded maximum average degree, we consider the problem of 2-distance coloring. This is the problem of coloring the vertices while ensuring that two vertices that are adjacent or have a common neighbor receive different colors. It is already known that planar graphs of girth at ...
A 2-tone coloring of a graph assigns two distinct colors to each vertex with the restriction that adjacent vertices have no common colors, and vertices at distance two have at most one common color. The 2-tone chromatic number of a graph is the minimum number of colors in any 2-tone col...
本期专栏为 “谱图理论” 系列的第26期,将介绍耶鲁大学教授、两届哥德尔奖得主 Daniel A. Spielman 所著图书 《Spectral and Algebraic Graph Theory》(电子版链接) 第二十六章 Ch 26: Planar Graphs 2, the Co…
The 2-distance coloring of graph G is a proper vertex coloring such that no two vertices at distance less than or equal to 2 in G are assigned the same color.We obtained a lower bound of 2-distance chromatic number of family of graphs with maximum degree Δ,χ2(Δ=d)≥(d2+1)2,d...
Improved text rendering at distance/in peripheral vision. Fixed frequency/amplitude of shader graph Gradient Noise node. Fixed issue with pink materials temporarily appearing on BakeToMesh particle systems. Fixed crash when using PolySpatial Image Based Light Receiver on Play to Device. ...
Let G be a graph with maximum degree △.The linear 2-arboricity of G,denoted by la_2(G),is the least integer k such that G can be decomposed into k edge disjoint forests,whose component trees are paths of length at most 2.In this note,we show that(1)for general planar graphs,la...
t-Relaxed 2-distant circular coloringDefective circular coloringOuterplanar graphNP-completeLet k be a positive integer. For any two integers i and j in \\(\\{0,1,\\ldots ,k-1\\}\\), let \\(|i-j|_k\\) be the circular distance between i and j, which is defined as \\(\\...
One version of this problem requires that processes within distance two of each other have different colors. This is known as the distance-2 coloring problem. We present a self-stabilizing algorithm for this problem that uses O(logΔ) memory on each node and that stabilizes in O(Δ2m) time...
A theta graph Θ2,1,2 is a graph obtained by joining two vertices by three internally disjoint paths of lengths 2, 1, and 2. A neighbor sum distinguishing (NSD) total coloring ϕ of G is a proper total coloring of G such that ∑z∈EG(u)∪{u}ϕ(z)≠∑