منابع مشابه
Bad News for Chordal Partitions
Reed and Seymour [1998] asked whether every graph has a partition into induced connected subgraphs such that each part is bipartite and the quotient graph is chordal. If true, this would have significant ramifications for Hadwiger’s Conjecture. We prove that the answer is ‘no’. In fact, we show that the answer is still ‘no’ for several relaxations of the question.
متن کاملList Partitions of Chordal Graphs
In an earlier paper we gave efficient algorithms for partitioning chordal graphs into k independent sets and l cliques. This is a natural generalization of the problem of recognizing split graphs, and is NPcomplete for graphs in general, unless k ≤ 2 and l ≤ 2. (Split graphs have k = l = 1.) In this paper we expand our focus and consider generalM -partitions, also known as trigraph homomorphism...
متن کاملVertex partitions of chordal graphs
A k-tree is a chordal graph with no (k + 2)-clique. An l-treepartition of a graph G is a vertex partition of G into ‘bags’, such that contracting each bag to a single vertex gives an l-tree (after deleting loops and replacing parallel edges by a single edge). We prove that for all k ≥ l ≥ 0, every k-tree has an l-tree-partition in which every bag induces a connected ⌊k/(l + 1)⌋-tree. An analogo...
متن کاملObstructions to partitions of chordal graphs
Matrix partition problems generalize graph colouring and homomorphism problems, and occur frequently in the study of perfect graphs. It is difficult to decide, even for a small matrix M , whether the M partition problem is polynomial time solvable or NP-complete (or possibly neither), and whether M -partitionable graphs can be characterized by a finite set of forbidden induced subgraphs (or per...
متن کاملList matrix partitions of chordal graphs
It is well known that a clique with k + 1 vertices is the only minimal obstruction to k-colourability of chordal graphs. A similar result is known for the existence of a cover by cliques. Both of these problems are in fact partition problems, restricted to chordal graphs. The first seeks partitions into k independent sets, and the second is equivalent to finding partitions into cliques. In an e...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2018
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22363