On Finding Lekkerkerker-Boland Subgraphs
نویسندگان
چکیده
Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a lineartime algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal forbidden submatrices of matrices that do not have the consecutive-ones property. We give a linear-time algorithm to find one in any matrix that does not have the consecutive-ones property.
منابع مشابه
On Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs
Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a lineartime algorithm to find one in any graph that is not an interval graph. Tucker characterized the minimal forbidden submatrices of matrices that do not have the consecutive-ones property. We give a linear-time algorithm to find one in any matrix that does not have the co...
متن کاملLinear-Time Algorithms for Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs
Tucker characterized the minimal forbidden submatrices of binary matrices that do not have the consecutive-ones property. We give a linear-time algorithm to find such a minimal one in any binary matrix that does not have the consecutive-ones property. Lekkerkerker and Boland characterized the minimal forbidden induced subgraphs for the class of interval graphs. We give a linear-time algorithm t...
متن کاملA generalization of the theorem of Lekkerkerker and Boland
Each fixed graph H gives rise to a list H-colouring problem. The complexity of list H-colouring problems has recently been fully classified: if H is a bi-arc graph, the problem is polynomial-time solvable, and otherwise it is NP-complete. The proof of this fact relies on a forbidden substructure characterization of bi-arc graphs, reminiscent of the theorem of Lekkerkerker and Boland on interval...
متن کاملObstructions to chordal circular-arc graphs of small independence number
A blocking quadruple (BQ) is a quadruple of vertices of a graph such that any two vertices of the quadruple either miss (have no neighbours on) some path connecting the remaining two vertices of the quadruple, or are connected by some path missed by the remaining two vertices. This is akin to the notion of asteroidal triple used in the classical characterization of interval graphs by Lekkerkerk...
متن کاملPath Graphs, Clique Trees, and Flowers
An asteroidal triple is a set of three independent vertices in a graph such that any two vertices in the set are connected by a path which avoids the neighbourhood of the third. A classical result by Lekkerkerker and Boland [10] showed that interval graphs are precisely the chordal graphs that do not have asteroidal triples. Interval graphs are chordal, as are the directed path graphs and the p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1303.1840 شماره
صفحات -
تاریخ انتشار 2013