5 citations · 15 across the 22 of their papers we have counts for
23 papers
On the number of 4-contractible edges in plane triangulations
Toshiki Abe, Michitaka Furuya, Raiji Mukae +1
In 2007, Ando and Egawa proved a theorem which provides a lower bound on the number of contractible edges preserving -connectedness in -connected graphs. In this paper, we re…
Forbidden subgraphs generating a finite set of graphs with minimum degree three and large girth
Yoshimi Egawa, Michitaka Furuya
For a family of graphs, a graph is said to be {\it -free} if contains no member of as an induced subgraph. We let $\tilde{\mathcal{…
A new strategy for finding spanning trees without small degree stems
Michitaka Furuya, Shoichi Tsuchiya
For an integer , a spanning tree of a graph without vertices of degree from to is called a {\it -ST} of the graph. The concept of -STs is a natural e…
Refinements of degree conditions for the existence of a spanning tree without small degree stems
Michitaka Furuya, Akira Saito, Shoichi Tsuchiya
A spanning tree of a graph without no vertices of degree is called a {\it homeomorphically irreducible spanning tree} (or a {\it HIST}) of the graph. Albertson, Berman, Hutchin…
Ramsey-type problems on induced covers and induced partitions toward the Gyárfás-Sumner conjecture
Shuya Chiba, Michitaka Furuya
Gyárfás and Sumner independently conjectured that for every tree , there exists a function such that every -free graph satisfies…
Ramsey-type results for path covers and path partitions. II. Digraphs
Shuya Chiba, Michitaka Furuya
Recently, the authors gave Ramsey-type results for the path cover/partition number of graphs. In this paper, we continue the research about them focusing on digraphs, and find a re…
Ramsey-type results for path covers and path partitions
Shuya Chiba, Michitaka Furuya
A family of subgraphs of is called a {\it path cover} (resp. a {\it path partition}) of if (resp. $\dot\bigcup _{P\in \…
A continuous generalization of domination-like invariants
Michitaka Furuya
In this paper, we define a new domination-like invariant of graphs. Let be the set of non-negative numbers. Let be a number, and let $G…
The uniqueness of covers for widely generalized line graphs
Michitaka Furuya, Sho Kubota, Tetsuji Taniguchi +1
As a natural generalization of line graphs, Hoffman line graphs were defined by Woo and Neumaier. Especially, Hoffman line graphs are closely related to the smallest eigenvalue of…
An algebraic reduction of Hedetniemi's conjecture
Ryoya Fukasaku, Michitaka Furuya, Akihiro Higashitani
For a graph , let denote the chromatic number. In graph theory, the following famous conjecture posed by Hedetniemi has been studied: For two graphs and , $χ(G\tim…
Small domination-type invariants in random graphs
Michitaka Furuya, Tamae Kawasaki
For and a graph , a function is called a -self dominating function of if for every vertex ,…
A Ramsey-type theorem for the matching number regarding connected graphs
Ilkyoo Choi, Michitaka Furuya, Ringi Kim +1
A major line of research is discovering Ramsey-type theorems, which are results of the following form: given a graph parameter , every graph with sufficiently large c…
A degree sum condition on the order, the connectivity and the independence number for Hamiltonicity
S. Chiba, M. Furuya, K. Ozeki +2
In [Graphs Combin.~24 (2008) 469--483.], the third author and the fifth author conjectured that if is a -connected graph such that …
Forbidden subgraphs for constant domination number
Michitaka Furuya
In this paper, we characterize the sets of connected graphs such that there exists a constant satisfying for every connected $\mathcal…
Sufficient conditions for the existence of a path-factor which are related to odd components
Yoshimi Egawa, Michitaka Furuya, Kenta Ozeki
In this paper, we are concerned with sufficient conditions for the existence of a -factor. We prove that for , there exists such th…
A characterization of domination weak bicritical graphs with large diameter
Michitaka Furuya
The domination number of a graph , denoted by , is the minimum cardinality of a dominating set of . A vertex of a graph is called critical if its deletion decreases the…
Path-factors involving paths of order seven and nine
Yoshimi Egawa, Michitaka Furuya
In this paper, we show the following two theorems (here is the number of components of with ): (i)~If a graph satisfies $c_{1}(G-X)+\frac{1}{3}…
Difference of forbidden pairs containing a claw
Guantao Chen, Michitaka Furuya, Songling Shan +2
When we study forbidden subgraph conditions guaranteeing graphs to have some properties, a claw (or ) frequently appears as one of forbidden subgraphs. Recently, Furuya an…
The existence of a path-factor without small odd paths
Yoshimi Egawa, Michitaka Furuya
In this paper, we show that if a graph satisfies for all , then has a -f…
A New Approach Towards a Conjecture on Intersecting Three Longest Paths
Shinya Fujita, Michitaka Furuya, Reza Naserasr +1
In 1966, T. Gallai asked whether every connected graph has a vertex that appears in all longest paths. Since then this question has attracted much attention and many work has been…
Dominating cycles and forbidden pairs containing a path of order 5
Shuya Chiba, Michitaka Furuya, Shoichi Tsuchiya
A cycle is a graph is dominating if every edge of the graph is incident with a vertex of the cycle. In this paper, we investigate the characterization of the class of the forbidden…
Forbidden pairs and the existence of a dominating cycle
Shuya Chiba, Michitaka Furuya, Shoichi Tsuchiya
A cycle in a graph is called dominating if every edge of the graph is incident with a vertex of the cycle. In this paper, we investigate forbidden pairs guaranteeing the existence…
Partitioning a graph into highly connected subgraphs
Valentin Borozan, Michael Ferrara, Shinya Fujita +4
Given , a -proper partition of a graph is a partition of such that each part of induces a -connected subgraph of . We…