Results 61 to 70 of about 511 (171)
Note on Hamiltonicity of Basis Graphs of Even Delta‐Matroids
Journal of Graph Theory, Volume 109, Issue 4, Page 446-453, August 2025.ABSTRACT We show that the basis graph of an even delta‐matroid is Hamiltonian if it has more than two vertices. More strongly, we prove that for two distinct edges e and f sharing a common end, it has a Hamiltonian cycle using e and avoiding f unless it has at most two vertices or it is a cycle of length at most four.
Donggyu Kim, Sang‐il Oum
wiley +1 more source
Subgraphs as circuits and bases of matroids
Discrete Mathematics, 1975 AbstractAs is well known, the cycles of any given graph G may be regarded as the circuits of a matroid defined on the edge set of G. The question of whether other families of connected graphs exist such that, given any graph G, the subgraphs of G isomorphic to some member of the family may be regarded as the circuits of a matroid defined on the edge ...
openaire +2 more sources
The structure of bases in bicircular matroids
Discrete Applied Mathematics, 1989 A generalized network flow problem (GNF) is a linear program with at most two nonzero entries in the constraint matrix; not exactly two, like in the pure network flow problem (PNF). Due to its special structure, even the former can be performed much faster than the general linear programming problems. A ``hidden'' PNF in an LP problem can be recognized
Randy Shull +3 more
openaire +2 more sources
On Serial Symmetric Exchanges of Matroid Bases [PDF]
Journal of Graph Theory, 2012 AbstractWe study some properties of a serial (i.e., one‐by‐one) symmetric exchange of elements of two disjoint bases of a matroid. We show that any two elements of one base have a serial symmetric exchange with some two elements of the other base. As a result, we obtain that any two disjoint bases in a matroid of rank 4 have a full serial symmetric ...
Daniel Kotlar, Ran Ziv
openaire +3 more sources
The e-Exchange Basis Graph and Matroid connectedness [PDF]
, 2018 Let\ud M\ud be a matroid and\ud e\ud ∈\ud E\ud (\ud M\ud ). The\ud e\ud -exchange basis\ud graph of\ud M\ud has vertices labeled by bases of\ud M\ud , and two vertices are\ud adjacent when the bases labeling them have symmetric difference\ud {\
Noble, Steven +3 more
core +1 more source
Generic root counts and flatness in tropical geometry
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract We use tropical and nonarchimedean geometry to study the generic number of solutions of families of polynomial equations over a parameter space Y$Y$. In particular, we are interested in the choices of parameters for which the generic root count is attained.
Paul Alexander Helminck, Yue Ren
wiley +1 more source
On Disjoint Common Bases in Two Matroids [PDF]
SIAM Journal on Discrete Mathematics, 2011 Summary: We prove two results on packing common bases of two matroids. First, we show that the computational problem of common base packing reduces to the special case where one of the matroids is a direct sum of uniform matroids. Second, we give a counterexample to a conjecture of Chow, which proposed a sufficient condition for the existence of a ...
Harvey, Nicholas J. A. +2 more
openaire +3 more sources
The Young matroid: A multiset extension of the Catalan matroid to arbitrary Young diagrams
, 2022 Introduced by Ardila (J. Combin. Theory Ser. A, 2003), the Catalan matroid is obtained by defining the bases of the matroid using Dyck paths from $(0,0)$ to $(n,n)$.
Dey, Hiranya Kishore +2 more
core
Efficient and strategy‐proof mechanism under general constraints
Theoretical Economics, Volume 20, Issue 2, Page 481-509, May 2025.This study investigates efficient and strategy‐proof mechanisms for allocating indivisible goods under constraints. First, we examine a setting without endowments. In this setting, we introduce a class of constraints—ordered accessibility—for which the serial dictatorship (SD) mechanism is Pareto‐efficient (PE), individually rational (IR), and group ...
Kenzo Imamura, Yasushi Kawase
wiley +1 more source
New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker +2 more
wiley +1 more source