Algorithmic graph theory and perfect graphs
نویسندگان
چکیده
منابع مشابه
Some problems in graph theory and graphs algorithmic theory
The Bermond-Thomassen conjecture states that, for any positive integer r, a digraph of minimum out-degree at least 2r − 1 contains at least r vertex-disjoint directed cycles. Thomassen proved that it is true when r = 2, and very recently the conjecture was proved for the case where r = 3. It is still open for larger values of r, even when restricted to (regular) tournaments. In this paper, we p...
متن کاملPerfect Graphs and the Perfect Graph Theorems
The theory of perfect graphs relates the concept of graph colorings to the concept of cliques. In this paper, we introduce the concept of a perfect graph as well as a number of graph classes that are always perfect. We next introduce both theWeak Perfect Graph Theorem and the Strong Perfect Graph Theorem and provide a proof of the Weak Perfect Graph Theorem. We also demonstrate an application o...
متن کاملSplit-Perfect Graphs: Characterizations and Algorithmic Use
Two graphs G and H with the same vertex set V are P4-isomorphic if every four vertices {a, b, c, d} ⊆ V induce a chordless path (denoted by P4) in G if and only if they induce a P4 in H. We call a graph split-perfect if it is P4-isomorphic to a split graph (i.e., a graph being partitionable into a clique and a stable set). This paper characterizes the new class of split-perfect graphs using the...
متن کاملGraph Searching & Perfect Graphs ∗
Perfect graphs, by definition, have a nice structure, that graph searching seems to extract in a, often non-inexpensive, manner. We scratch the surface of this elegant research area by giving two examples: Lexicographic Breadth Search on Chordal Graphs, and Lexicographic Depth First Search on Cocomparability graphs.
متن کاملAlgorithmic graph theory
Introduction to graphs, Paths, cycles and trails Max-flow min-cut theorem, computing max s-t flows and min-cut Edge and Vertex Connectivity and Menger's theorem Maximum matching, Hall's theorem, algorithms for computing maximum matching in weighted and unweighted graphs. Edge and vertex colouring of graphs. Independent sets Planar graphs and algorithms for checking for planarity. The course nee...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1980
ISSN: 0377-0427
DOI: 10.1016/0771-050x(80)90036-4