A new characterization of unichord-free graphs

نویسنده

  • Terry A. McKee
چکیده

Unichord-free graphs are defined as having no cycle with a unique chord. They have appeared in several papers recently and are also characterized by minimal separators always inducing edgeless subgraphs (in contrast to characterizing chordal graphs by minimal separators always inducing complete subgraphs). A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Complexity of colouring problems restricted to unichord-free and \{square, unichord\}-free graphs

A unichord in a graph is an edge that is the unique chord of a cycle. A square is an induced cycle on four vertices. A graph is unichord-free if none of its edges is a unichord. We give a slight restatement of a known structure theorem for unichord-free graphs and use it to show that, with the only exception of the complete graph K4, every square-free, unichord-free graph of maximum degree 3 ca...

متن کامل

$\chi$-bounds, operations and chords

A long unichord in a graph is an edge that is the unique chord of some cycle of length at least 5. A graph is long-unichord-free if it does not contain any long-unichord. We prove a structure theorem for long-unichord-free graph. We give an O(nm)-time algorithm to recognize them. We show that any long-unichord-free graph G can be colored with at most O(ω) colors, where ω is the maximum number o...

متن کامل

$C_4$-free zero-divisor graphs

‎In this paper we give a characterization for all commutative‎ ‎rings with $1$ whose zero-divisor graphs are $C_4$-free.‎

متن کامل

A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION

‎The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$‎. ‎In this case‎, ‎$B$ is called a textit{metric basis} for $G$‎. ‎The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$‎. ‎Givi...

متن کامل

Associated Graphs of Modules Over Commutative Rings

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper we introduce a new graph associated to modules over commutative rings. We study the relationship between the algebraic properties of modules and their associated graphs. A topological characterization for the completeness of the special subgraphs is presented. Also modules whose associated graph is complete...

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discussiones Mathematicae Graph Theory

دوره 35  شماره 

صفحات  -

تاریخ انتشار 2015