Morteza Hasanvand

activity

20162025

most citedThe List Square Coloring Conjecture fails for bipartite planar graphs and their line graphs

2 citations · 4 across the 22 of their papers we have counts for

collaborators

22 papers

math.CO2025

On the existence of minimally tough graphs having large minimum degrees

Morteza Hasanvand

Kriesel conjectured that every minimally $1$ -tough graph has a vertex with degree precisely $2$ . Katona and Varga (2018) proposed a generalized version of this conjecture which say…

math.CO2024

Equitable factorizations of highly edge-connected graphs: complete characterizations

Morteza Hasanvand

In this paper, we show that every highly edge-connected graph $G$ , under a necessary and sufficient degree condition, can be edge-decomposed into $k$ factors $G_{1}, \dots, G_{k}$ such…

math.CO2022★ 2 cited

The List Square Coloring Conjecture fails for bipartite planar graphs and their line graphs

Morteza Hasanvand

Kostochka and Woodall (2001) conjectured that the square of every graph has the same chromatic number and list chromatic number. In 2015 Kim and Park disproved this conjecture for…

math.CO2022

The existence of tree-connected ${g, f}$ -factors in edge-connected graphs and tough graphs

Morteza Hasanvand

In 1970 Lov{á}sz gave a necessary and sufficient condition for the existence of a factor $F$ in a graph $G$ such that for each vertex $v$ , $g (v) \leq d_{F} (v) \leq f (v)$ , where $g$ and $…

math.CO2022

Toughness and the existence of tree-connected ${f, f + k}$ -factors

Morteza Hasanvand

Let $G$ be a graph and let $f$ be a positive integer-valued function on $V (G)$ satisfying $2 m \leq f \leq b$ , where $b$ and $m$ are two positive integers with $b \geq 4 m^{2}$ . In this pape…

math.CO2022

Highly tree-connected complementary modulo factors with bounded degrees

Morteza Hasanvand

Let $G$ be a bipartite graph with bipartition $(X, Y)$ , let $k$ be a positive integer, and let $f : V (G) \to Z_{k}$ be a mapping with $\sum_{v\in X}f(v) \stackrel{k}{\equiv}\sum_…

math.CO2022

The existence of planar $4$ -connected essentially $6$ -edge-connected graphs with no claw-decompositions

Morteza Hasanvand

In 2006 Bar{á}t and Thomassen conjectured that every planar $4$ -edge-connected $4$ -regular simple graph of size divisible by three admits a claw-decomposition. Later, Lai (2007) di…

math.CO2022

The existence of ${p, q}$ -orientations in edge-connected graphs

Morteza Hasanvand

In 1976 Frank and Gy{á}rf{á}s gave a necessary and sufficient condition for the existence of an orientation in an arbitrary graph $G$ such that for each vertex $v$ , the out-degree…

math.CO2022

The existence of $m$ -tree-connected $(g, f + f^{'} - m)$ -factors using $(g, f)$ -factors and $m$ -tree-connected $(m, f^{'})$ -factors

Morteza Hasanvand

Let $G$ be a graph and let $g$ , $f$ , and $f^{'}$ be three positive integer-valued functions on $V (G)$ with $g \leq f$ . Tokuda, Xu, and Wang (2003) showed that if $G$ contains a $(g, f)$ -…

math.CO2022

Edge-decompositions of $O (m)$ -edge-connected graphs into isomorphic copies of a fixed tree of size $m$

Morteza Hasanvand

In this paper, we show that every $O (m)$ -edge-connected simple graph $G$ of size divisible by $m$ with minimum degree at least $2^{O (m)}$ has an edge-decomposition into isomorphic…

math.CO2022

Modulo factors with bounded degrees

Morteza Hasanvand

Let $G$ be a bipartite graph with bipartition $(X, Y)$ , let $k$ be a positive integer, and let $f : V (G) \to {- 1, \dots, k - 2}$ be a mapping with $\sum_{v\in X}f(v) \stackrel{…

math.CO2022

Spanning tree-connected subgraphs with small degrees

Morteza Hasanvand

Let $G$ be a graph with a spanning subgraph $F$ , let $m$ be a positive integer, and let $f$ be a positive integer-valued function on $V (G)$ . In this paper, we show that if for all…

math.CO2021

The existence of uniform hypergraphs for which interpolation property of complete coloring fails

Nastaran Haghparast, Morteza Hasanvand, Yumiko Ohno

In 1967 Harary, Hedetniemi, and Prins showed that every graph $G$ admits a complete $t$ -coloring for every $t$ with $χ (G) \leq t \leq ψ (G)$ , where $χ (G)$ denotes the chromatic number…

math.CO2019

Equitable factorizations of edge-connected graphs

Morteza Hasanvand

In this paper, we show that every $(3 k - 3)$ -edge-connected graph $G$ , under a certain condition on whose degrees, can be edge-decomposed into $k$ factors $G_{1}, \dots, G_{k}$ such that…

math.CO2019

Bipartite partition-connected factors with small degrees

Morteza Hasanvand

In this paper, we show that every $2 m$ -partition-connected graph $G$ has a bipartite $m$ -partition-connected factor $H$ such that for each vertex $v$ , $d_H(v)\le \lceil \frac{3}{4}…

math.CO2018

Factors and connected factors in tough graphs with high isolated toughness

Morteza Hasanvand

Let $G$ be a graph and let $f$ be a positive integer-valued function on $V (G)$ . Assume that for all $S \subseteq V (G)$ , $v \in I (G ∖ S) \sum f (v) (f (v) + 1) \leq ∣ S ∣,$ where $I(…

math.CO2018

Packing spanning rigid subgraphs with restricted degrees

Morteza Hasanvand

Let $G$ be a graph and let $l$ be an integer-valued function on subsets of $V (G)$ . The graph $G$ is said to be $l$ -partition-connected, if for every partition $P$ of $V (G)$ , $e_G(P…

math.CO2018★ 1 cited

Packing spanning partition-connected subgraphs with small degrees

Morteza Hasanvand

Let $G$ be a graph with $X \subseteq V (G)$ and let $l$ be an intersecting supermodular subadditive integer-valued function on subsets of $V (G)$ . The graph $G$ is said to be $l$ -part…

math.CO2017★ 1 cited

Spanning closed walks with bounded maximum degrees of graphs on surfaces

Morteza Hasanvand

Gao and Richter (1994) showed that every $3$ -connected graph which embeds on the plane or the projective plane has a spanning closed walk meeting each vertex at most $2$ times. Bru…

math.CO2017

Modulo orientations with bounded out-degrees

Morteza Hasanvand

Let $G$ be a graph, let $k$ be a positive integer, and let $p : V (G) \to Z_{k}$ be a mapping with $∣ E (G) ∣ \equiv k \sum_{v \in V (G)} p (v)$ . In this paper, we show that…

math.CO2017

Spanning trees and spanning closed walks with small degrees

Morteza Hasanvand

Let $G$ be a graph and let $f$ be a positive integer-valued function on $V (G)$ . In this paper, we show that if for all $S \subseteq V (G)$ , $ω(G\setminus S)<\sum_{v\in S}(f(v)-2)+2+ω…

math.CO2016

Tutte's $3$ -Flow Conjecture in $3$ -tree-connected graphs

Morteza Hasanvand

Tutte's $3$ -flow conjecture says that every $4$ -edge-connected graph admits a nowhere-zero $3$ -flow. Kochol (2001) showed that it is enough to prove this conjecture for $5$ -edge-co…

On the existence of minimally tough graphs having large minimum degrees

Equitable factorizations of highly edge-connected graphs: complete characterizations

The List Square Coloring Conjecture fails for bipartite planar graphs and their line graphs

The existence of tree-connected {g,f}-factors in edge-connected graphs and tough graphs

Toughness and the existence of tree-connected {f,f+k}-factors

Highly tree-connected complementary modulo factors with bounded degrees

The existence of planar 4-connected essentially 6-edge-connected graphs with no claw-decompositions

The existence of {p,q}-orientations in edge-connected graphs

The existence of m-tree-connected (g,f+f′−m)-factors using (g,f)-factors and m-tree-connected (m,f′)-factors

Edge-decompositions of O(m)-edge-connected graphs into isomorphic copies of a fixed tree of size m

Modulo factors with bounded degrees

Spanning tree-connected subgraphs with small degrees

The existence of uniform hypergraphs for which interpolation property of complete coloring fails

Equitable factorizations of edge-connected graphs

Bipartite partition-connected factors with small degrees

Factors and connected factors in tough graphs with high isolated toughness

Packing spanning rigid subgraphs with restricted degrees

Packing spanning partition-connected subgraphs with small degrees

Spanning closed walks with bounded maximum degrees of graphs on surfaces

Modulo orientations with bounded out-degrees

Spanning trees and spanning closed walks with small degrees

Tutte's 3-Flow Conjecture in 3-tree-connected graphs

The existence of tree-connected ${g, f}$ -factors in edge-connected graphs and tough graphs

Toughness and the existence of tree-connected ${f, f + k}$ -factors

The existence of planar $4$ -connected essentially $6$ -edge-connected graphs with no claw-decompositions

The existence of ${p, q}$ -orientations in edge-connected graphs

The existence of $m$ -tree-connected $(g, f + f^{'} - m)$ -factors using $(g, f)$ -factors and $m$ -tree-connected $(m, f^{'})$ -factors

Edge-decompositions of $O (m)$ -edge-connected graphs into isomorphic copies of a fixed tree of size $m$

Tutte's $3$ -Flow Conjecture in $3$ -tree-connected graphs