ColoringproperProper Proper coloringcoloringdoi:10.1007/1-4020-0611-X_820An assignment of colors to nodes in a graph in which adjacent nodes are colored differently. Graph theory .Springer USEncyclopedia of Operations Research & Management Science...
Mathematics - Number Theory05C15We present a simpler proof of a bound on the number of proper colorings of a graph that was obtained recently by Liu and Murty using Tur'an sieve (in fact, we prove a stronger inequality). We also point out that these results are subsumed in a stronger ...
An edge-colored directed graph is called properly connected if, between every pair of vertices, there is a properly colored directed path. We study some conditions on directed graphs which guarantee the existence of a coloring that is properly connected. We also study conditions on a colored dire...
The Greatest Number of Proper 2-colorings of a (v,e) Graph and the Extremal Graphs 来自 知网 喜欢 0 阅读量: 46 作者: X Chen 摘要: Let P (G, λ ) denote the chromatic polynomial of a graph G.For given positive integers v, e and λ, let f (v, e, λ) = max (P (G,...
for which the question of 3-colorability can be decided in polynomial time and, if so, a proper 3-coloring can be determined also in polynomial time... B Randerath,I Schiermeyer - 《Discrete Applied Mathematics》 被引量: 192发表: 2004年 Hyperchaotic behaviour of two bi-directionally coupled...
For p ∈ N, a coloring A of the vertices of a graph G is p-centered if for every connected subgraph H of G, either H receives more than p colors under λ or there is a color that appears exactly once in H. Centered colorings play an important role in the theory of sparse graphs...
For fixed integers k 2, and for n-element sets X and colorings Delta: [X] k Gamma! f0; 1; : : :g where every color class is a matching and has cardinality at most u, we show that there exists a totally multicolored subset Y ` X with jY j max ( c 1 Delta ` n k u ' ...
The planar graph 3-colorability (P3C) is one of NP-complete prob- lem. Duo to probably appearing the second type of mistake in setting colors, a computational algorithm might repeat many times to decide whether it can correct wrong coloring in many examined subgraphs. Then one can turn P3C ...
-coloring decision problem (respectively, function problem) is that of deciding the existence of (respectively, finding) a proper k -coloring of a given input graph. in this context, we can also define the maximum proper k -colorable induced subgraph problem as the problem of finding a ...
The minimum number of colors required in a proper-path (trail, walk) coloring is referred to as the proper-path (trail, walk) connection number of G. In J. Bang-Jensen, T. Bellitto and A. Yeo, Proper-walk connection number of graphs, J. Graph Theory 96(2020) 137鈥 159, the ...