Related papers: Ribbon graph minors and low-genus partial duals
In this paper, we first introduce the notions of checkerboard colourable minors for ribbon graphs motivated by the Eulerian ribbon graph minors, and two kinds of bipartite minors for ribbon graphs, one of which is the dual of the…
Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They computed these two partial-dual genus polynomials of four families of ribbon graphs, posed some research…
Partial duality is a duality of ribbon graphs relative to a subset of their edges generalizing the classical Euler-Poincare duality. This operation often changes the genus. Recently J.L.Gross, T.Mansour, and T.W.Tucker formulated a…
In this paper we consider minors of ribbon graphs (or, equivalently, cellularly embedded graphs). The theory of minors of ribbon graphs differs from that of graphs in that contracting loops is necessary and doing this can create additional…
Gross, Mansour and Tucker introduced the partial-dual orientable genus polynomial and the partial-dual Euler genus polynomial. They showed that the partial-dual genus polynomial for an orientable ribbon graph is interpolating and gave an…
Huggett and Moffatt characterized all bipartite partial duals of a plane graph in terms of all-crossing directions of its medial graph. Then Metsidik and Jin characterized all Eulerian partial duals of a plane graph in terms of…
Recently, Chmutov introduced the partial duality of ribbon graphs, which can be regarded as a generalization of the classical Euler-Poincar\'e duality. The partial-dual genus polynomial $^\partial\varepsilon_G(z)$ is an enumeration of the…
The geometric dual of a cellularly embedded graph is a fundamental concept in graph theory and also appears in many other branches of mathematics. The partial dual is an essential generalization which can be obtained by forming the…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
In 2009, Chmutov introduced the partial-duality for a ribbon graph $G$. Recently, Gross, Mansour and Tucker enumerated all possible partial-duals of $G$ by genus and introduced the partial-dual genus polynomial of a ribbon graph $G.$ This…
Graphs that are critical (minimal excluded minors) for embeddability in surfaces are studied. In Part I we consider the structure of graphs with a 2-vertex-cut that are critical with respect to the Euler genus. A general theorem describing…
It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented…
Recently, Dasbach, Futer, Kalfagianni, Lin, and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or equivalently, embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon…
Recently, Gross, Mansour and Tucker introduced the partial-dual genus polynomial of a ribbon graph as a generating function that enumerates the partial duals of the ribbon graph by genus. It is analogous to the extensively-studied…
Recently, Gross, Mansour and Tucker introduced the partial-twuality polynomials. In this paper, we find that when there are enough parallel edges, any multiple graph is a negative answer to the problem 8.7 in their paper [European J.…
In the present work we are going to give a formal exposition of the ribbon graphs topic based on notes of Labourie \cite{Lab}, since is difficult to find as such in the literature.
Recently, Gross, Mansour, and Tucker introduced the partial Petrial polynomial, which enumerates all partial Petrials of a ribbon graph by Euler genus. They provided formulas or recursions for various families of ribbon graphs, including…
We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S_3^{|E(G)|},…
In this note we show that any embedded graph has a checkerboard colourable twisted dual and any Eulerian embedded graph has a checkerboard colourable partial Petrial, answering questions posed by Ellis-Monaghan and Moffatt. The proofs are…
We develop an algebraic framework for ribbon graphs, revealing symmetry properties of (partial) twisted duality. The original ribbon group action of Ellis-Monaghan and Moffatt restricts self-duality, -petriality, or -triality to the…