Publication

Characterizing Path Graphs by Forbidden Induced Subgraphs

2009
Journal Articles

Abstract

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. (C) 2009 Wiley Periodicals, Inc. J Graph Theory 62: 369-384, 2009

Official source

https://infoscience.epfl.ch/entities/publication/fdda6bd3-351c-4370-a0a7-67e3f5fa8d27

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2009
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/fdda6bd3-351c-4370-a0a7-67e3f5fa8d27

About this result

Ontological neighbourhood

Mathematics

Discrete mathematics: Graph theory

Related concepts (32)

Line graph

In the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. L(G) is constructed in the following way: for each edge in G, make a vertex in L(G); for every two edges in G that have a vertex in common, make an edge between their corresponding vertices in L(G). The name line graph comes from a paper by although both and used the construction before this.

Chordal graph

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree.

Induced path

In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence of vertices in G such that each two adjacent vertices in the sequence are connected by an edge in G, and each two nonadjacent vertices in the sequence are not connected by any edge in G. An induced path is sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem.

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