This thesis consists of two parts. In the second part the research papers that constitute the
new results of the thesis are presented. In this first part we want to put these results in a …

A graph G is (k, l) if its vertex set can be partitioned into at most k independent sets and l
cliques. The (k, l)-Graph Sandwich Problem asks, given two graphs G1=(V, E1) and G2=(V …

Golumbic, Kaplan, and Shamir, in their paper [MC Golumbic, H. Kaplan, R. Shamir, Graph
sandwich problems, J. Algorithms 19 (1995) 449–473] on graph sandwich problems …

The Clay Mathematics Institute has selected seven Millennium Problems to motivate
research on important classic questions that have resisted solution over the years. Among …

In this work, we show that the class of word-representable graphs is closed under split
recomposition and determine the representation number of the graph obtained by …

The P4-sparse Graph Sandwich Problem asks, given two graphs G1=(V, E1) and G2=(V,
E2), whether there exists a graph G=(V, E) such that E1⊆ E⊆ E2 and G is P4-sparse. In this …

A sandwich problem for property Π asks whether there exists a sandwich graph of a given
pair of graphs which has the desired property Π. Graph sandwich problems were first …

The polynomial dichotomy for three nonempty part sandwich problems - ScienceDirect Skip to
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List partitions generalize list colourings. Sandwich problems generalize recognition
problems. The polynomial dichotomy (NP-complete versus polynomial) of list partition …

Sandwich problems generalize graph recognition problems with respect to a property Π. A
recognition problem has a graph as input, whereas a sandwich problem has two graphs as …