Characterization Of Graphic Matroids Research Articles

A Characterization of Graphic Matroids Based on Circuit Orderings

It is shown that a binary matroid is graphic if and only if it does not contain a cyclically ordered circuit and two cocircuits that interact in a particular way. This result generalizes a theorem ...

On Mighton's characterization of graphic matroids

Mighton (2008) [5] recently gave a new characterization of graphic matroids. This note combines Mighton's approach with a result of Cunningham (1982) [4] to provide a shorter, more direct proof of Mighton's result.

A new characterization of graphic matroids

We give a necessary and sufficient condition for a binary matroid to be graphic. The condition is very natural, but, unlike other similar results, it gives a trivial algorithm for testing graphicness.

On internally 4-connected non-regular binary matroids

We prove that every internally 4-connected non-regular binary matroid other than F 7 and F 7 ∗ has one of the following matroids as a minor: K 5 , K 5 ∗ , N 10, T 12⧹ e and T 12/ e. As corollaries, we prove a theorem related to Tutte's characterization of graphic matroids and a conjecture by Dharmatilake on excluded minors for the class of binary matroids with branch-width at most 3.

On Tutt's Characterization of graphic matroids—a graphic proof

AbstractIn this paper we present a relatively simple proof of Tutt's characterization of graphic matroids. The proof uses the notion of ‘signed graph’ and it is ‘graphic’ in the sense that it can be presented almost entirely by drawing (signed) graphs. © 1995 John Wiley & Sons, Inc.