Nowhere-zero 3-flows in matroid base graph

Let [Formula: see text] be the edge ideal of a bicyclic graph [Formula: see text] with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of [Formula: see text] in terms of the induced matching number of [Formula: see text]. For the base case of this family of graphs, i.e. dumbbell graphs, we explicitly compute the induced matching number. Moreover, we prove that [Formula: see text], for all [Formula: see text], when [Formula: see text] is a dumbbell graph with a connecting path having no more than two vertices.

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Matroid base polytope decomposition II: Sequences of hyperplane splits

Advances in Applied Mathematics ◽

10.1016/j.aam.2013.11.003 ◽

2014 ◽

Vol 54 ◽

pp. 121-136 ◽

Cited By ~ 2

Author(s):

Vanessa Chatelain ◽

Jorge Luis Ramírez Alfonsín

Keyword(s):

Matroid Base

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Weighted Zeta Functions of Graph Coverings

The Electronic Journal of Combinatorics ◽

10.37236/1117 ◽

2006 ◽

Vol 13 (1) ◽

Author(s):

Iwao Sato

Keyword(s):

Zeta Function ◽

Zeta Functions ◽

Equivalence Classes ◽

Signed Graphs ◽

Base Graph ◽

Regular Covering ◽

Decomposition Formula ◽

Graph Coverings

We present a decomposition formula for the weighted zeta function of an irregular covering of a graph by its weighted $L$-functions. Moreover, we give a factorization of the weighted zeta function of an (irregular or regular) covering of a graph by equivalence classes of prime, reduced cycles of the base graph. As an application, we discuss the structure of balanced coverings of signed graphs.

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Small Subgraphs in the Trace of a Random Walk

The Electronic Journal of Combinatorics ◽

10.37236/6169 ◽

2017 ◽

Vol 24 (1) ◽

Author(s):

Michael Krivelevich ◽

Peleg Michaeli

Keyword(s):

Random Walk ◽

Random Graph ◽

Complete Graph ◽

Combinatorial Properties ◽

Base Graph

We consider the combinatorial properties of the trace of a random walk on the complete graph and on the random graph $G(n,p)$. In particular, we study the appearance of a fixed subgraph in the trace. We prove that for a subgraph containing a cycle, the threshold for its appearance in the trace of a random walk of length $m$ is essentially equal to the threshold for its appearance in the random graph drawn from $G(n,m)$. In the case where the base graph is the complete graph, we show that a fixed forest appears in the trace typically much earlier than it appears in $G(n,m)$.

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On distances in generalized Sierpiński graphs

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm160802001e ◽

2018 ◽

Vol 12 (1) ◽

pp. 49-69 ◽

Cited By ~ 2

Author(s):

Alejandro Estrada-Moreno ◽

Erick Rodríguez-Bazan ◽

Juan Rodríguez-Velázquez

Keyword(s):

Explicit Formula ◽

Recursive Formula ◽

Arbitrary Vertex ◽

Base Graph ◽

Sierpiński Graphs ◽

Recursive Formulas

In this paper we propose formulas for the distance between vertices of a generalized Sierpi?ski graph S(G, t) in terms of the distance between vertices of the base graph G. In particular, we deduce a recursive formula for the distance between an arbitrary vertex and an extreme vertex of S(G, t), and we obtain a recursive formula for the distance between two arbitrary vertices of S(G, t) when the base graph is triangle-free. From these recursive formulas, we provide algorithms to compute the distance between vertices of S(G, t). In addition, we give an explicit formula for the diameter and radius of S(G, t) when the base graph is a tree.

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Morphological Analysis by Surface Patterns and by Graph

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i3.4.16775 ◽

2018 ◽

Vol 7 (3.4) ◽

pp. 204

Author(s):

Iazzi Said ◽

Yousfi Abdellah ◽

Bellafkih Mostafa ◽

Aboutajdine Driss

Keyword(s):

Morphological Analysis ◽

Base Graph ◽

Surface Patterns

In this article, we propose a comparison between our two morphological analyzers, which we have developed in recent years. The first is based on surface patterns Arabic words, the second is an analyzer which combines Buckwalter approach and the approach of morphological analysis in base graph. The comparison is made on a corpus of 1400 Arabic words that generalize all cases of Arabic derived words. The results obtained show the interest and the advantages of each analyzer.

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