Coloring graphs is one of important and frequently used topics in diverse sciences. In the majority of the articles, it is intended to find a proper bound for vertex coloring, edge coloring or total coloring in the graph. Although it is important to find a proper algorithm for graph coloring, it is hard and time-consuming too. In this paper, a new algorithm for vertex coloring, edge coloring an...

A module of an undirected graph is a set X of nodes such for each node x not in X , either every member of X is adjacent to x, or no member of X is adjacent to x. There is a canonical linear-space representation for the modules of a graph, called the modular decomposition. Closely related to modular decomposition is the transitive orientation problem, which is the problem of assigning a directi...

4-methylimidazole (4-mei) is a simple nitrogen-containing heterocyclic compound, and recently classified as group 2b by international agency for research on cancer (iarc). caramel coloring is widely applied food coloring in many food products including coffee, carbonated beverages, beer and wine. in present study, ɣ-irradiation was applied to caramel color iii to reduce the level of 4-mei witho...

Structural graph parameters, such as treewidth, pathwidth, and clique-width, are a central topic of study in parameterized complexity. A main aim research this area is to understand the “price generality” these widths: we transition from more restrictive general notions, which problems that see their complexity status deteriorate fixed-parameter tractable (FPT) intractable? This type question b...

4-Methylimidazole (4-MEI) is a simple nitrogen-containing heterocyclic compound, and recently classified as group 2B by International Agency for Research on Cancer (IARC). Caramel coloring is widely applied food coloring in many food products including coffee, carbonated beverages, beer and wine. In present study, ɣ-irradiation was applied to Caramel Color III to reduce the level of 4-MEI witho...

a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...

A graph is (P5,gem)-free, when it does not contain P5 (an induced path with five vertices) or a gem (a graph formed by making an universal vertex adjacent to each of the four vertices of the induced path P4) as an induced subgraph. We present O(n2) time recognition algorithms for chordal gem-free and for (P5,gem)free graphs. Using a characterization of (P5,gem)-free graphs by their prime graphs...

In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannancontractions dened on modular spaces endowed with a graph. We do not impose the Δ2-conditionor the Fatou property on the modular spaces to give generalizations of some recent results. Thegiven results play as a modular version of metric xed point results.

We prove that for any partition of the plane into a closed set C and an open set O and for any configuration T of three points, there is a translated and rotated copy of T contained in C or in O. Apart from that, we consider partitions of the plane into two sets whose common boundary is a union of piecewise linear curves. We show that for any such partition and any configuration T which is a ve...