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...
In this coloring, every directed path will be strongly proper. It is easy to see that the digraph Strongly Proper Connected Coloring of Graphs 801 Figure 1. An exemplary ear decomposition ED = {P1, P2, P3, P4} of some graph with cycles of length divisible by 3 (P1 is a cycle with ...
We also observe that Minimum Coloring is NP-complete already on ⌞-EPG, which follows from a proof for B1-EPG in Epstein et al. (2013). Finally, we provide efficient constant-factor-approximation algorithms for each of these problems on B1-EPG graphs. Hyperideal-based intersection graphs ...
While Builder tries to force Painter to build some fixed monochromatic graph H, Builder cannot choose edges arbitrarily. He has to keep the constructed graph in a prescribed class of finite graphs G throughout the game. The task is to determine the winner for a given pair H,G. They showed...
For graphs F and H, where H has chromatic index t, the proper Ramsey number PR(F, H) is the smallest positive integer n such that every i-edge coloring of K_n results in a monochromatic Fora properly colored H. The proper Ramsey number PR{F, H) is investigated for certain pairs F...
F. Lazebnik, New upper bounds for the greatest number of proper color- ings of a (v, e)-graph, J. Graph Theory 14 (1990) 25-29.F. Lazebnik. New upper bounds for the greatest number of proper colorings of a (v,e)-graph. J. Graph Theory, 14(1):25-29, 1990....
proper-path coloringstrong proper-path coloringLet G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of P are colored the same. If P is a proper u − v path of length d(u, v), then P is a proper u − v geodesic. An edge ...
NUMBER theoryA defective vertex coloring of a graph is a coloring in which some adjacent vertices may have the same color. An edge whose adjacent vertices have the same color is called a bad edge. A defective coloring of a graph G with minimum possible number of bad edges in G...
Our research is motivated by the conjecture proposed in a recent paper of Gastineau and Togni on S $S$‐packing edge‐colorings asserting that, for subcubic graphs, by allowing three additional induced matchings, one is able to save one matching color. We prove that every graph with maximum...
NUMBER theoryMAGICMOTIVATION (Psychology)A coloring f: V (G) -> {1, 2, . . ., k} is called a magic sigma coloring of G if the sum of colors of all the vertices in the neighborhood of each vertex of G is the same. A graph that admits such a coloring is said to be magic ...