Shoichi Tsuchiya

Plane Triangulations Without a Spanning Halin Subgraph: Counterexamples to the Lovász--Plummer Conjecture on Halin Graphs

A \sl Halin graph is a simple plane graph consisting of a tree without degree 2 vertices and a cycle induced by the leaves of the tree. In 1975, Lovasz and Plummer conjectured that every 4-connected plane triangulation has a spanning Halin subgraph. In this paper, we construct an infinite family of counterexamples to the conjecture.

Forbidden pairs and the existence of a dominating cycle

A cycle C in a graph G is called dominating if every edge of G is incident with a vertex of C . For a set H of connected graphs, a graph G is said to be H -free if G does not contain any member of H as an induced subgraph. When | H | = 2 , H is called a forbidden pair. In this paper, we investigate the set H of forbidden pairs H which satisfies that every 2-connected H -free graph has a dominating cycle. In particular, we show that H is a very small class and find some maximal forbidden pairs of H .

Distance-restricted matching extendability of fullerene graphs

A fullerene graph is a 3-connected cubic plane graph whose all faces are bounded by 5- or 6-cycles. In this paper, we show that a matching M of a fullerene graph can be extended to a perfect matching if the following hold: (i) three faces around each vertex in

Plane Triangulations Without a Spanning Halin Subgraph II

\{x,y:xy\in M\}

A Characterization of

{x,y:xy∈M} are bounded by 6-cycles and (ii) the edges in M lie at distance at least 13 pairwise.

K_{2,4}

Tutte showed that

-Minor-Free Graphs

4

Dominating Cycles and Forbidden Pairs Containing

-connected planar graphs are Hamiltonian, but it is well known that