4 research outputs found
On the hardness of recognizing triangular line graphs
Given a graph G, its triangular line graph is the graph T(G) with vertex set
consisting of the edges of G and adjacencies between edges that are incident in
G as well as being within a common triangle. Graphs with a representation as
the triangular line graph of some graph G are triangular line graphs, which
have been studied under many names including anti-Gallai graphs, 2-in-3 graphs,
and link graphs. While closely related to line graphs, triangular line graphs
have been difficult to understand and characterize. Van Bang Le asked if
recognizing triangular line graphs has an efficient algorithm or is
computationally complex. We answer this question by proving that the complexity
of recognizing triangular line graphs is NP-complete via a reduction from
3-SAT.Comment: 18 pages, 8 figures, 4 table
Research Naval Postgraduate School, v.4, no. 14, October 2012
NPS Research is published by the Research and Sponsored Programs, Office of the Vice President and Dean of Research, in accordance with NAVSOP-35. Views and opinions expressed are not necessarily those of the Department of the Navy.Approved for public release; distribution is unlimited
On an Edge Partition and Root Graphs of Some Classes of Line Graphs
The Gallai and the anti-Gallai graphs of a graph are complementary pairs of spanning subgraphs of the line graph of . In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph into the edge sets of the Gallai and anti-Gallai graphs of . Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed