New advances about a conjecture on Helly circle graphs
نویسندگان
چکیده
A circle graph is the intersection graph of a set of chords on a circle. A graph is Helly circle if there is a model of chords satisfying the Helly property. In 2003 it was conjectured that Helly circle graphs are exactly diamond-free circle graphs. In this work, we propose a method to compress any Helly circle representation of a graph and give some ideas to advance in an inductive proof of the diamond conjecture.
منابع مشابه
Some new results on circle graphs
Abstract: The intersection graph of a set of chords on a circle is called a circle graph. This class of graphs admits some interesting subclasses, such as: Helly circle graphs, clique-Helly circle graphs, unit circle graphs and proper circular-arc graphs. In this paper, we prove some inclusion relations among these subclasses. A necessary condition for a graph being a Helly circle graph is show...
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 18 شماره
صفحات -
تاریخ انتشار 2004