Zh. G. Nikoghosyan

activity

20082023

most citedA Size Bound for Hamilton Cycles

4 citations · 17 across the 31 of their papers we have counts for

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31 papers · 1 filter

math.CO2023

Large Cycles in Graphs Around Conjectures of Bondy and Jung -- Modifications and Sharpness

Zhora Nikoghosyan

A number of new sufficient conditions for generalized cycles (large cycles including Hamilton and dominating cycles as special cases) in an arbitrary $k$ -connected graph $(k=1,2,..…

math.CO2022★ 1 cited

A Note on Large Cycles in Graphs Around Conjectures of Bondy and Jung

Zhora Nikoghosyan

Two new sufficient conditions for generalized cycles (including Hamilton and dominating cycles as special cases) in an arbitrary k-connected graph (k=1,2,...) are derived, which pr…

math.CO2021

New Ore-type Conditions for Hamilton Cycles and Spanning Trees with few leaves

Zhora Nikoghosyan

New Ore-type conditions for Hamilton cycles and spanning trees with few leaves are presented.

math.CO2017

On Pure Degree Sequence Manipulations Forcing Long Cycles in Graphs

Zhora Nikoghosyan

The well-known Hamiltonian sufficient conditions, proposed by Dirac, Faudree et al., Pósa, Bondy, Chvátal are based on pure degree manipulations without any additional conditions.…

math.CO2016

On Dirac's Conjecture

Zh. G. Nikoghosyan

Let $G$ be a 2-connected graph, $l$ be the length of a longest path in $G$ and $c$ be the circumference - the length of a longest cycle in $G$ . In 1952, Dirac proved that $c>\sqrt{…

math.CO2015

Spanning trees in connected graphs with few branch and end vertices

Zhora Nikoghosyan

A vertex of degree one in a tree is called an end vertex and a vertex of degree at least three is called a branch vertex. For a graph $G$ , let $σ_{2}$ be the minimum degree sum of tw…

math.CO2014

On $k$ -ended spanning and dominating trees

Zh. G. Nikoghosyan

A tree with at most $k$ leaves is called a $k$ -ended tree. A spanning 2-ended tree is a Hamilton path. A Hamilton cycle can be considered as a spanning 1-ended tree. The earliest r…

math.CO2014

On large $k$ -ended trees in connected graphs

Zh. G. Nikoghosyan

A vertex of degree one is called an end-vertex, and an end-vertex of a tree is called a leaf. A tree with at most $k$ leaves is called a $k$ -ended tree. For a positive integer $k$ ,…

math.CO2014

On Relative Length of Long Paths and Cycles in Graphs

Zh. G. Nikoghosyan

Let $G$ be a graph on $n$ vertices, $p$ the order of a longest path and $κ$ the connectivity of $G$ . In 1989, Bauer, Broersma Li and Veldman proved that if $G$ is a 2-connected gra…

math.CO2014

Relative Length of Long Paths and Cycles in Graphs

Zh. G. Nikoghosyan

For a graph $G$ , $n$ denotes the order of $G$ , $p$ the order of a longest path in $G$ and $c$ the order of a longest cycle. We show that if $G$ is a 2-connected graph such that $d(…

math.CO2014

On some Versions of Conjectures of Bondy and Jung

Zh. G. Nikoghosyan

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to wel…

math.CO2014

A Common Generalization of Dirac's two Theorems

Zh. G. Nikoghosyan

Let $G$ be a 2-connected graph of order $n$ and let $c$ be the circumference - the order of a longest cycle in $G$ . In this paper we present a sharp lower bound for the circumferen…

math.CO2014★ 4 cited

Long Cycles in 1-tough Graphs

Zh. G. Nikoghosyan

In 1952, Dirac proved that every 2-connected graph with minimum degree $δ$ either is hamiltonian or contains a cycle of length at least $2 δ$ . In 1986, Bauer and Schmeichel enlarged…

math.CO2012★ 1 cited

A Note on Hamilton Cycles

Zh. G. Nikoghosyan

If $G$ is a more than one tough graph on $n$ vertices with $δ \geq \frac{n}{2} - a$ for a given $a > 0$ and $n$ is large enough then $G$ is hamiltonian.

math.CO2012

Nonhamiltonian Graphs with Given Toughness

Zh. G. Nikoghosyan

In 1973, Chvátal introduced the concept of toughness $τ$ of a graph and constructed an infinite class of nonhamiltonian graphs with $τ = 3/2$ . Later Thomassen found nonhamiltonian gr…

math.CO2012

Disconnected Forbidden Subgraphs, Toughness and Hamilton Cycles

Zh. G. Nikoghosyan

In 1974, Goodman and Hedetniemi proved that every 2-connected $(K_{1, 3}, K_{1, 3} + e)$ -free graph is hamiltonian. This result gave rise many other hamiltonicity conditions for various…

math.CO2012

Evolutionary Hamiltonian Graph Theory

Zh. G. Nikoghosyan

We present an alternative domain concerning mathematics to investigate universal evolution mechanisms by focusing on large cycles theory (LCT) - a simplified version of well-known…

math.CO2012

A Sharp Bound for the Circumference in $t$ -tough graphs with $t > 1$

Zh. G. Nikoghosyan

It is proved that if $G$ is a $t$ -tough graph of order $n$ and minimum degree $δ$ with $t > 1$ then either $G$ has a cycle of length at least $min {n, 2 δ + 5}$ or $G$ is the Petersen…

math.CO2012

My Research Visiting Card in Hamiltonian Graph Theory

Zh. G. Nikoghosyan

We present eighteen exact analogs of six well-known fundamental Theorems (due to Dirac, Nash-Williams and Jung) in hamiltonian graph theory providing alternative compositions of gr…

math.CO2012

Hamilton and long cycles in $t$ -tough graphs with $t > 1$

Zh. G. Nikoghosyan

It is proved that if $G$ is a $t$ -tough graph of order $n$ and minimum degree $δ$ with $t > 1$ then either $G$ has a cycle of length at least $min {n, 2 δ + 4}$ or $G$ is the Petersen…

math.CO2012

Degree Conditions for Dominating Cycles in 1-tough Graphs

Zh. G. Nikoghosyan

We prove: (i) if $G$ is a 1-tough graph of order $n$ and minimum degree $δ$ with $δ \geq (n - 2) /3$ then each longest cycle in $G$ is a dominating cycle unless $G$ belongs to an easily…

math.CO2012

A Degree Condition for Dominating Cycles in $t$ -tough Graphs with $t > 1$

Zh. G. Nikoghosyan

Let $G$ be a $t$ -tough graph of order $n$ and minimum degree $δ$ with $t > 1$ . It is proved that if $δ \geq (n - 2) /3$ then each longest cycle in $G$ is a dominating cycle.

math.CO2011

A Size Upper Bound for Dominating Cycles

Zh. G. Nikoghosyan

Recently it was shown (by the author) that every graph of size $q$ (the number of edges) and minimum degree $δ$ is hamiltonian if $q \leq δ^{2} + δ - 1$ (arXiv:1107.2201v1). In this paper w…

math.CO2011★ 4 cited

A Size Bound for Hamilton Cycles

Zh. G. Nikoghosyan

Every graph of size $q$ (the number of edges) and minimum degree $δ$ is hamiltonian if $q \leq δ^{2} + δ - 1$ . The result is sharp.

Large Cycles in Graphs Around Conjectures of Bondy and Jung -- Modifications and Sharpness

A Note on Large Cycles in Graphs Around Conjectures of Bondy and Jung

New Ore-type Conditions for Hamilton Cycles and Spanning Trees with few leaves

On Pure Degree Sequence Manipulations Forcing Long Cycles in Graphs

On Dirac's Conjecture

Spanning trees in connected graphs with few branch and end vertices

On k-ended spanning and dominating trees

On large k-ended trees in connected graphs

On Relative Length of Long Paths and Cycles in Graphs

Relative Length of Long Paths and Cycles in Graphs

On some Versions of Conjectures of Bondy and Jung

A Common Generalization of Dirac's two Theorems

Long Cycles in 1-tough Graphs

A Note on Hamilton Cycles

Nonhamiltonian Graphs with Given Toughness

Disconnected Forbidden Subgraphs, Toughness and Hamilton Cycles

Evolutionary Hamiltonian Graph Theory

A Sharp Bound for the Circumference in t-tough graphs with t>1

My Research Visiting Card in Hamiltonian Graph Theory

Hamilton and long cycles in t-tough graphs with t>1

Degree Conditions for Dominating Cycles in 1-tough Graphs

A Degree Condition for Dominating Cycles in t-tough Graphs with t>1

A Size Upper Bound for Dominating Cycles

A Size Bound for Hamilton Cycles

On $k$ -ended spanning and dominating trees

On large $k$ -ended trees in connected graphs

A Sharp Bound for the Circumference in $t$ -tough graphs with $t > 1$

Hamilton and long cycles in $t$ -tough graphs with $t > 1$

A Degree Condition for Dominating Cycles in $t$ -tough Graphs with $t > 1$