Related papers: Constructing a Tutte polynomial for graphs embedde…
A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we…
The surface Tutte polynomial has recently been generalised to pseudo-surfaces equipping it with recursive deletion-contraction relations. We use these relations to show that this generalisation naturally possesses a quasi-tree expansion.…
Tutte showed that a graph $G$ is planar if and only if the conflict graph associated to every cycle of $G$ is bipartite. We define a (not necessarily unique) signed conflict graph associated to a maximally planar subgraph of a nonplanar…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
We describe a construction of the Tutte polynomial for both matroids and $q$-matroids based on an appropriate partition of the underlying support lattice into intervals that correspond to prime-free minors, which we call a Tutte partition.…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
A cycle $C$ in a graph $G$ is called a Tutte cycle if, after deleting $C$ from $G$, each component has at most three neighbors on $C$. Tutte cycles play an important role in the study of Hamiltonicity of planar graphs. Thomas and Yu and…
We relate matroid connectivity to Tutte-connectivity in an infinite graph. Moreover, we show that the two cycle matroids, the finite-cycle matroid and the cycle matroid, in which also infinite cycles are taken into account, have the same…
Polynomials on stranded graphs are higher dimensional generalization of Tutte and Bollob\'as-Riordan polynomials [Math. Ann. 323 (2002), 81-96]. Here, we deepen the analysis of the polynomial invariant defined on rank 3 weakly-colored…
The automorphisms of a graph act naturally on its set of labeled imbeddings to produce its unlabeled imbeddings. The imbedding sum of a graph is a polynomial that contains useful information about a graph's labeled and unlabeled imbeddings.…
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a…
Tittmann, Averbouch and Makowsky [P. Tittmann, I. Averbouch, J.A. Makowsky, The enumeration of vertex induced subgraphs with respect to the number of components, European Journal of Combinatorics, 32 (2011) 954-974], introduced the subgraph…
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…
In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete…
This is a chapter destined for the book "Handbook of the Tutte Polynomial". The chapter is a composite. The first part is a brief introduction to Orlik-Solomon algebras. The second part sketches the theory of evaluative functions on matroid…
Due to their flexibility to represent almost any kind of relational data, graph-based models have enjoyed a tremendous success over the past decades. While graphs are inherently only combinatorial objects, however, many prominent analysis…
In this note we study some of the properties of the generating polynomial for homomorphisms from a graph to at complete weighted graph on $q$ vertices. We discuss how this polynomial relates to a long list of other well known graph…
We show that any graph polynomial from a wide class of graph polynomials yields a recurrence relation on an infinite class of families of graphs. The recurrence relations we obtain have coefficients which themselves satisfy linear…
A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. Almost embeddings (more precisely, their higher-dimensional analogues) naturally appear in…
We present a new edge selection heuristic and vertex ordering heuristic that together enable one to compute the Tutte polynomial of much larger sparse graphs than was previously doable. As a specific example, we are able to compute the…