On Polar, Trivially Perfect Graphs
نویسندگان
چکیده
منابع مشابه
A new characterization of trivially perfect graphs
A graph G is trivially perfect if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) α(G) equals the number of (maximal) cliques m(G). We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.
متن کاملProbe threshold and probe trivially perfect graphs
7 An undirected graph G = (V,E) is a probe C graph if its vertex set can be partitioned 8 into two sets, N (non-probes) and P (probes) where N is independent and there 9 exists E′ ⊆ N × N such that G′ = (V,E ∪ E′) is a C graph. In this article we 10 investigate probe threshold and probe trivially perfect graphs and characterise them 11 in terms of certain 2-Sat formulas and in other ways. For t...
متن کاملComputing square roots of trivially perfect and threshold graphs
A graph H is a square root of a graph G if two vertices are adjacent in G if and only if they are at distance one or two in H . Computing a square root of a given graph is NP-hard, even when the input graph is restricted to be chordal. In this paper, we show that computing a square root can be done in linear time for a well-known subclass of chordal graphs, the class of trivially perfect graphs...
متن کاملLinear-time certifying algorithms for recognizing trivially perfect graphs
We give the first linear-time certifying algorithms to recognize trivially perfect graphs, with sublinear certificates for negative output. In case of membership in the class of trivially perfect graphs, our algorithms provide as certificate a structure for the input graph that characterizes the class, and in case of non-membership they provide as certificate a forbidden induced subgraph of the...
متن کاملOn Critically Perfect Graphs on Critically Perfect Graphs
A perfect graph is critical if the deletion of any edge results in an imperfect graph. We give examples of such graphs and prove some basic properties. We relate critically perfect graphs to well-known classes of perfect graphs, investigate the structure of the class of critically perfect graphs, and study operations preserving critical perfectness.
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: International Journal of Computers Communications & Control
سال: 2010
ISSN: 1841-9836,1841-9836
DOI: 10.15837/ijccc.2010.5.2257