Results 91 to 100 of about 235,748 (327)
A simple recurrence formula for the number of rooted maps on surfaces by edges and genus [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We establish a simple recurrence formula for the number $Q_g^n$ of rooted orientable maps counted by edges and genus. The formula is a consequence of the KP equation for the generating function of bipartite maps, coupled with a Tutte equation, and it was
Sean Carrell, Guillaume Chapuy
doaj +1 more source
Borel chain conditions of Borel posets [PDF]
arXiv, 2021 We study the coarse classification of partial orderings using chain conditions in the context of descriptive combinatorics. We show that (unlike the Borel counterpart of many other combinatorics), we have a distinct hierarchy of different chain conditions, similar to the classical case.
arxiv
Alexander Duality and Rational Associahedra [PDF]
, 2013 A recent pair of papers of Armstrong, Loehr, and Warrington and Armstrong, Williams, and the author initiated the systematic study of {\em rational Catalan combinatorics} which is a generalization of Fuss-Catalan combinatorics (which is in turn a ...
Rhoades, Brendon
core
Independent Sets of Random Trees and Sparse Random Graphs
Journal of Graph Theory, EarlyView.ABSTRACT An independent set of size k $k$ in a finite undirected graph G $G$ is a set of k $k$ vertices of the graph, no two of which are connected by an edge. Let xk ( G ) ${x}_{k}(G)$ be the number of independent sets of size k $k$ in the graph G $G$ and let α ( G ) = max { k ≥ 0 : x k ( G ) ≠ 0 } $\alpha (G)=\max \{k\ge 0:{x}_{k}(G)\ne 0\}$. In 1987,
Steven Heilman
wiley +1 more source
Generalized Rainbow Connection of Graphs and their Complements
Discussiones Mathematicae Graph Theory, 2018 Let G be an edge-colored connected graph. A path P in G is called ℓ-rainbow if each subpath of length at most ℓ + 1 is rainbow. The graph G is called (k, ℓ)-rainbow connected if there is an edge-coloring such that every pair of distinct vertices of G is ...
Li Xueliang +3 more
doaj +1 more source
Lecture notes on algebraic methods in combinatorics [PDF]
arXiv, 2023 These are lecture notes of a course taken in Leipzig 2023, spring semester. It deals with extremal combinatorics, algebraic methods and combinatorial geometry. These are not meant to be exhaustive, and do not contain many proofs that were presented in the course.
arxiv
Conformal Hypergraphs: Duality and Implications for the Upper Clique Transversal Problem
Journal of Graph Theory, EarlyView.ABSTRACT Given a hypergraph H ${\rm{ {\mathcal H} }}$, the dual hypergraph of H ${\rm{ {\mathcal H} }}$ is the hypergraph of all minimal transversals of H ${\rm{ {\mathcal H} }}$. The dual hypergraph is always Sperner, that is, no hyperedge contains another.
Endre Boros +3 more
wiley +1 more source
, 2019 The classical theory of symmetric functions has a central position in algebraic combinatorics, bridging aspects of representation theory, combinatorics, and enumerative geometry.
Allen Hatcher +36 more
core +1 more source
Combinatorics and Physics [PDF]
, 2011 Item does not contain ...
Ebrahimi-Fard, K. +2 more
openaire +3 more sources
Weighted Turán Theorems With Applications to Ramsey‐Turán Type of Problems
Journal of Graph Theory, EarlyView.ABSTRACT We study extensions of Turán Theorem in edge‐weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique containing it. These problems are motivated by Ramsey‐Turán type problems.
József Balogh +2 more
wiley +1 more source