This chapter discusses the structure of Composition, the partial order of Graphs and Homomorphisms, and testing for the Existence of Homomorphism.Expand

There are several apparently independent sources and algorithmic solutions of the minimum spanning tree problem and their motivations, and they have appeared in Czechoslovakia, France, and Poland, going back to the beginning of this century.Expand

A linear-time algorithm to recognize and represent proper circular-arc graphs and obtain a new proof of a characterization of proper interval graphs by forbidden subgraphs.Expand

It is shown that the list homomorphism problem is polynomial time solvable if the complement of H is a circular arc graph of clique covering number two, and is NP-complete otherwise.Expand

A polynomial time algorithm is given to solve the problem when the input graph is an interval graph and it is argued that the complexity of certain other modifications of the problem are likely to be difficult to classify.Expand

A. Vince introduced a natural generalization of graph coloring and proved some basic facts, revealing it to be a concept of interest. His work relies on continuous methods. In this note we make someâ€¦ Expand

We prove that the complements of interval bigraphs are precisely those circular arc graphs of clique covering number two, which admit a representation without two arcs covering the whole circle. Weâ€¦ Expand

It is shown that packing a maximum number of independent triangles is polynomial-time solvable for many classes of structured graphs, including weakly chordal graphs, asteroidal triple-free graphs, polygon-circle graphs, and interval-filament graphs.Expand