The objective of the present paper is to study maximum radius r a connected graph order n, minimum degree δ ≥ 2 and girth at least g 4. Erdős, Pach, Pollack Tuza proved that if = 4, is, triangle-free, then ≤ n − + 12, noted up value additive constant, this upper bound tight. In we shall determine exact maximum. For larger values little known. We settle for 6 , 8 prove an every even g, which con...

In this paper, we prove that a linear block code with girth 2( t +1) is -sequential-recovery locally repairable codes (LRCs) locality xmlns:xlink="http://www.w3.org/1999/xlink">r if its parity-check matrix has column weight at least 2 and row most +1. This gives new connection between seque...

the objective followed in the present study was to survey the relationship between 18 body trait measurements (live weight, height at wither, paunch girth, neck diameter, body length, girth around the body, width of fat tail at above, below and midpoint of fat tail, fat tail length lowers right and left sides, fat tail gap length, fat tail depth at the above, below, and midpoint, and girth arou...

Morris and Saxton used the method of containers to bound number n-vertex graphs with m edges containing no ℓ-cycles, hence girth more than ℓ. We consider a generalization r-uniform hypergraphs. The hypergraph H is minimum ℓ ≥ 2 such that there exist distinct vertices v 1 , … hyperedges e i + ∈ for all ≤ Letting N r ( n ) denote hypergraphs larger defining λ = ⌈ − ∕ ⌉ we show which tight when di...

Let G be an r-regular graph of order n and independence number α(G). We show that if G has odd girth 2k + 3 then α(G) ≥ n1−1/kr1/k . We also prove similar results for graphs which are not regular. Using these results we improve on the lower bound of Monien and Speckenmeyer, for the independence number of a graph of order n and odd girth 2k + 3. AMS Subject Classification. 05C15 §

It was proved in [Z. Dvořàk, D. Kràl, P. Nejedlỳ, R. Škrekovski, Coloring squares of planar graphs with girth six, European J. Combin. 29 (4) (2008) 838–849] that every planar graph with girth g ≥ 6 and maximum degree ∆ ≥ 8821 is 2-distance (∆ + 2)-colorable. We prove that every planar graph with g ≥ 6 and∆ ≥ 18 is 2-distance (∆+ 2)-colorable. © 2009 Elsevier B.V. All rights reserved.