scholarly journals Tight lower bounds on the matching number in a graph with given maximum degree

2018 ◽  
Vol 89 (2) ◽  
pp. 115-149 ◽  
Author(s):  
Michael A. Henning ◽  
Anders Yeo
Keyword(s):  
Lower Bounds ◽  
Maximum Degree ◽  
Matching Number

Lower bounds of graph energy in terms of matching number

2018 ◽  
Vol 549 ◽  
pp. 276-286 ◽  
Author(s):  
Dein Wong ◽  
Xinlei Wang ◽  
Rui Chu
Keyword(s):  
Lower Bounds ◽  
Matching Number ◽  
Graph Energy

Randomly coloring graphs with lower bounds on girth and maximum degree

2003 ◽  
Vol 23 (2) ◽  
pp. 167-179 ◽  
Author(s):  
Martin Dyer ◽  
Alan Frieze
Keyword(s):  
Lower Bounds ◽  
Maximum Degree

scholarly journals Remarks on upper and lower bounds formatching sequencibility of graphs

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2091-2099
Author(s):  
Shuya Chiba ◽  
Yuji Nakano
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Maximum Degree ◽  
Edge Coloring ◽  
Hamilton Cycle ◽  
Upper And Lower Bounds ◽  
Linear Ordering ◽  
The Relationship

In 2008, Alspach [The Wonderful Walecki Construction, Bull. Inst. Combin. Appl. 52 (2008) 7-20] defined the matching sequencibility of a graph G to be the largest integer k such that there exists a linear ordering of its edges so that every k consecutive edges in the linear ordering form a matching of G, which is denoted by ms(G). In this paper, we show that every graph G of size q and maximum degree ? satisfies 1/2?q/?+1? ? ms(G) ? ?q?1/??1? by using the edge-coloring of G, and we also improve this lower bound for some particular graphs. We further discuss the relationship between the matching sequencibility and a conjecture of Seymour about the existence of the kth power of a Hamilton cycle.

scholarly journals New Bounds for Topological Indices on Trees through Generalized Methods

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1097 ◽  
Author(s):  
Álvaro Martínez-Pérez ◽  
José M. Rodríguez
Keyword(s):  
Large Class ◽  
Lower Bounds ◽  
Maximum Degree ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Upper And Lower Bounds ◽  
Unified Approach ◽  
Wide Family ◽  
New Inequalities

Topological indices are useful for predicting the physicochemical behavior of chemical compounds. A main problem in this topic is finding good bounds for the indices, usually when some parameters of the graph are known. The aim of this paper is to use a unified approach in order to obtain several new inequalities for a wide family of topological indices restricted to trees and to characterize the corresponding extremal trees. The main results give upper and lower bounds for a large class of topological indices on trees, fixing or not the maximum degree. This class includes the first variable Zagreb, the Narumi–Katayama, the modified Narumi–Katayama and the Wiener index.

scholarly journals Maximum number of edges in claw-free graphs whose maximum degree and matching number are bounded

2017 ◽  
Vol 340 (5) ◽  
pp. 927-934 ◽  
Author(s):  
Cemil Dibek ◽  
Tınaz Ekim ◽  
Pinar Heggernes
Keyword(s):  
Maximum Degree ◽  
Matching Number

Interval Packing and Covering in the Boolean Lattice

1996 ◽  
Vol 5 (4) ◽  
pp. 373-384 ◽  
Author(s):  
Konrad Engel
Keyword(s):  
Lower Bounds ◽  
Pairwise Disjoint ◽  
Boolean Lattice ◽  
Covering Number ◽  
Matching Number ◽  
Packing And Covering ◽  
Minimum Number ◽  
Fractional Numbers

Let be the hypergraph whose points are the subsets X of [n] := {1,…,n} with l≤ |X| ≤ u, l < u, and whose edges are intervals in the Boolean lattice of the form I = {C ⊆[n] : X⊆C⊆Y} where |X| = l, |Y| = u, X ⊆ Y.We study the matching number i.e. the the maximum number of pairwise disjoint edges, and the covering number i.e. the minimum number of points which cover all edges. We prove that max and that for every ε > 0 the inequalities hold, where for the lower bounds we suppose that n is not too small. The corresponding fractional numbers can be determined exactly. Moreover, we show by construction that

Girth and Independence Ratio

1982 ◽  
Vol 25 (2) ◽  
pp. 179-186 ◽  
Author(s):  
Glenn Hopkins ◽  
William Staton
Keyword(s):  
Lower Bounds ◽  
Maximum Degree ◽  
Cubic Graphs

AbstractLower bounds are given for the independence ratio in graphs satisfying certain girth and maximum degree requirements. In particular, the independence ratio of a graph with maximum degree Δ and girth at least six is at least (2Δ − 1)/(Δ2 + 2Δ − 1). Sharper bounds are given for cubic graphs.

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