… A graph IS called matroidal if the binary relation “equab to or forms a … of the node packings
of a matroidal graph from the other incidence … We call such a graph a strict matroidal graph.. …

… this the circuitmatroid and its dual the bond-matroid of G. In … matroid structure, for a given
matroid M to be graphic (cographic), that is the bond-matroid (circuitmatroid) of some finite graph…

… system IG is a matroid iff G is an M-graph. Let K be the set of all M-graphs. Since a l-edge …
But then “WEEGk' We have proved that Gk is an M-graph and (8) is a matroidal decomposition. …

… A matroid may be defined as a collection of sets, called bases, which satisfy a certain exchange
axiom. The basis graph of a matroid … Two characterizations of basis graphs are obtained. …

… The tree graph T(M) of a matroid M has the bases of M as its points, with two of … The smallest
matroid Mo which is not graphical has L … For this matroid, the tree graph is shown in Fig. …

… In paticular if G is a graph, the cycles of M(G) are the edge sets of eulerian subgraphs (we
call a graph eulerian if every vertex has even degree). If M is a regular matroid 31 …

… To conclude we observe that if we can obtain graphs corresponding to the Y-components of
a graphic matroid M we can construct from them a graph corresponding to M. The necessary …

… Two graphs that play an important role in matroid theory, and indeed … We denote this
matroid by Um,n and call it the uniform matroid of rank m on an n-element set. Clearly …

… Finally, we establish the relationship between graphs that give rise to the same graphic
matroid, and conclude with a handy procedure for deciding whether a certain 1-element binary …

… ) graph matroid. We will identify the ground set of a bipartite graph matroid with the complete
bipartite graph, and … the ground set of a graph matroid with the complete graph, writing Kn = …