Color-line and Proper Color-line Graphs
Van Bang Le, Florian Pfender

TL;DR
This paper introduces color-line graphs, generalizing line graphs with edge coloring, provides characterizations, and analyzes the computational complexity of recognizing such graphs under various coloring constraints.
Contribution
It defines color-line graphs, offers Krausz-type characterizations, and establishes complexity results for recognizing these graphs with fixed color bounds.
Findings
Recognition of color-line graphs with at most k colors is NP-complete for general graphs.
Recognition of properly edge-colored color-line graphs with at most k colors is polynomial.
Linear time recognition algorithm for proper 2-color line graphs.
Abstract
Motivated by investigations of rainbow matchings in edge colored graphs, we introduce the notion of color-line graphs that generalizes the classical concept of line graphs in a natural way. Let be a (properly) edge-colored graph. The (proper) color-line graph of has edges of as vertices, and two edges of are adjacent in if they are incident in or have the same color. We give Krausz-type characterizations for (proper) color-line graphs, and point out that, for any fixed , recognizing if a graph is the color-line graph of some graph in which the edges are colored with at most colors is NP-complete. In contrast, we show that, for any fixed , recognizing color-line graphs of properly edge colored graphs with at most colors is polynomially. Moreover, we give a good characterization for proper -color line graphs that yields…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
