Improper Twin Edge Coloring of Graphs
Paniz Abedin, Saieed Akbari, Marc Demange, Tinaz Ekim

TL;DR
This paper introduces the concept of improper twin edge coloring in graphs, establishing the conditions under which the minimum number of colors equals the chromatic number, and proves the problem's computational complexity.
Contribution
It characterizes the improper twin chromatic index for graphs, showing it equals the vertex chromatic number except in specific cases, and proves the NP-hardness of related decision problems.
Findings
The improper twin chromatic index equals the vertex chromatic number unless (G)=2 mod 4.
Deciding whether '_{it}(G) equals (G) or (G)+1 is NP-hard.
Polynomial-time solutions exist for certain perfect graph classes.
Abstract
Let be a graph whose each component has order at least 3. Let for some integer be an improper edge coloring of (where adjacent edges may be assigned the same color). If the induced vertex coloring defined by (where the indicated sum is computed in and denotes the set of all edges incident to ) results in a proper vertex coloring of , then we refer to such a coloring as an improper twin -edge coloring. The minimum for which has an improper twin -edge coloring is called the improper twin chromatic index of and is denoted by . In this paper, we show that if is a graph with vertex chromatic number , then , unless and in this case…
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Advanced Graph Theory Research
