Searcharxiv⌕ Search

arXiv subjects

Shuya Chiba

Publications and source records attributed to Shuya Chiba.

13 recordsLinked to original sources
arXiv2025

Hydrogen-induced fast fracture in a 1.5 GPa dual-phase steel

This study clarifies the hydrogen embrittlement (HE) behavior in a 1.5 GPa ferrite-martensite dual-phase (DP) steel. Hydrogen pre-charging (3.8 mass ppm diffusible hydrogen), followed by slow strain tensile testing (10-4 s-1), resulted in a brittle fracture at 900 MPa within the elastic regime. Fractographic studies indicated that surface crack initiation consists of intergranular and quasi-cleavage morphology; site-specific transmission electron microscopy (TEM) investigations revealed sub-surface secondary crack blunting by ferrite. A mixed-mode morphology consisting of ductile and brittle features was observed adjacent to crack initiation. It differs from the previous investigation of uncharged DP steel, wherein a predominant brittle fracture was observed. Following significant crack growth, the pre-charged specimen exhibited predominant brittle fracture; site-specific TEM and transmission Kikuchi diffraction studies revealed {100} ferrite cleavage cracking. Electron backscatter diffraction studies were performed on the cross-sectional cracks. We explain the HE via hydrogen-induced fast fracture mechanism. During loading, hydrogen diffuses to the prior austenite grain boundary, resulting in hydrogen-induced decohesion. Subsequent hydrogen diffusion to the crack tip promotes brittle fracture at high crack velocity (>Vcrit). The high crack velocity effectively inhibits crack blunting via dislocation emission, ensuring sustained brittle crack growth even after hydrogen depletion at the crack tip, resulting in {100} ferrite cleavage cracking. Based on TEM observations, we explain the formation of river pattern features on the {100} cleavage surface.

cond-mat.mtrl-sci↗
arXiv2024

Ramsey-type problems on induced covers and induced partitions toward the Gyárfás-Sumner conjecture

Gyárfás and Sumner independently conjectured that for every tree $T$, there exists a function $f_{T}:\mathbb{N}\rightarrow \mathbb{N}$ such that every $T$-free graph $G$ satisfies $χ(G)\leq f_{T}(ω(G))$, where $χ(G)$ and $ω(G)$ are the {\it chromatic number} and the {\it clique number} of $G$, respectively. This conjecture gives a solution of a Ramsey-type problem on the chromatic number. For a graph $G$, the {\it induced SP-cover number ${\rm inspc}(G)$} (resp. the {\it induced SP-partition number ${\rm inspp}(G)$}) of $G$ is the minimum cardinality of a family $\mathcal{P}$ of induced subgraphs of $G$ such that each element of $\mathcal{P}$ is a star or a path and $\bigcup _{P\in \mathcal{P}}V(P)=V(G)$ (resp. $\dot\bigcup _{P\in \mathcal{P}}V(P)=V(G)$). Such two invariants are directly related concepts to the chromatic number. From the viewpoint of this fact, we focus on Ramsey-type problems for two invariants ${\rm inspc}$ and ${\rm inspp}$, which are analogies of the Gyárfás-Sumner conjecture, and settle them. As a corollary of our results, we also settle other Ramsey-type problems for widely studied invariants.

math.CO↗
arXiv2021

Ramsey-type results for path covers and path partitions. II. Digraphs

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 relationship between the path cover/partition number and forbidden structures in digraphs. Let $D$ be a weakly connected digraph. A family $\mathcal{P}$ of subdigraphs of $D$ is called a {\it path cover} (resp. a {\it path partition}) of $D$ if $\bigcup _{P\in \mathcal{P}}V(P)=V(D)$ (resp. $\dot\bigcup _{P\in \mathcal{P}}V(P)=V(D)$) and every element of $\mathcal{P}$ is a directed path. The minimum cardinality of a path cover (resp. a path partition) of $D$ is denoted by ${\rm pc}(D)$ (resp. ${\rm pp}(D)$). In this paper, we find forbidden structure conditions assuring us that ${\rm pc}(D)$ (or ${\rm pp}(D)$) is bounded by a constant.

math.CO↗
arXiv2021

Ramsey-type results for path covers and path partitions

A family $\mathcal{P}$ of subgraphs of $G$ is called a {\it path cover} (resp. a {\it path partition}) of $G$ if $\bigcup _{P\in \mathcal{P}}V(P)=V(G)$ (resp. $\dot\bigcup _{P\in \mathcal{P}}V(P)=V(G)$) and every element of $\mathcal{P}$ is a path. The minimum cardinality of a path cover (resp. a path partition) of $G$ is denoted by ${\rm pc}(G)$ (resp. ${\rm pp}(G)$). In this paper, we characterize the forbidden subgraph conditions assuring us that ${\rm pc}(G)$ (or ${\rm pp}(G)$) is bounded by a constant. Our main results introduce a new Ramsey-type problem.

math.CO↗
arXiv2018

Partitioning a graph into cycles with a specified number of chords

For a graph $G$, let $σ_{2}(G)$ be the minimum degree sum of two non-adjacent vertices in $G$. A chord of a cycle in a graph $G$ is an edge of $G$ joining two non-consecutive vertices of the cycle. In this paper, we prove the following result, which is an extension of a result of Brandt et al. (J. Graph Theory 24 (1997) 165-173) for large graphs: For positive integers $k$ and $c$, there exists an integer $f(k,c)$ such that, if $G$ is a graph of order $n \ge f(k, c)$ and $σ_{2}(G) \ge n$, then $G$ can be partitioned into $k$ vertex-disjoint cycles, each of which has at least $c$ chords.

math.CO↗
arXiv2018

Induced nets and Hamiltonicity of claw-free graphs

The connected graph of degree sequence 3,3,3,1,1,1 is called a net, and the vertices of degree 1 in a net is called its endvertices. Broersma conjectured in 1993 that a 2-connected graph G with no induced K_{1,3} is hamiltonian if every endvertex of each induced net of G has degree at least (|V(G)|-2)/3. In this paper we prove this conjecture in the affirmative.

math.CO↗
arXiv2017

On directed 2-factors in digraphs and 2-factors containing perfect matchings in bipartite graphs

In this paper, we give the following result: If $D$ is a digraph of order $n$, and if $d_{D}^{+}(u) + d_{D}^{-}(v) \ge n$ for every two distinct vertices $u$ and $v$ with $(u, v) \notin A(D)$, then $D$ has a directed $2$-factor with exactly $k$ directed cycles of length at least $3$, where $n \ge 12k+3$. This result is equivalent to the following result: If $G$ is a balanced bipartite graph of order $2n$ with partite sets $X$ and $Y$, and if $d_{G}(x)+d_{G}(y) \ge n + 2$ for every two vertices $x \in X$ and $y \in Y$ with $xy \notin E(G)$, then for every perfect matching $M$, $G$ has a $2$-factor with exactly $k$ cycles of length at least $6$ containing every edge of $M$, where $n \ge 12k+3$. These results are generalizations of theorems concerning Hamilton cycles due to Woodall (1972) and Las Vergnas (1972), respectively.

math.CO↗
arXiv2017

On degree sum conditions for 2-factors with a prescribed number of cycles

For a vertex subset $X$ of a graph $G$, let $Δ_{t}(X)$ be the maximum value of the degree sums of the subsets of $X$ of size $t$. In this paper, we prove the following result: Let $k$ be a positive integer, and let $G$ be an $m$-connected graph of order $n \ge 5k - 2$. If $Δ_{2}(X) \ge n$ for every independent set $X$ of size $\lceil m/k \rceil+1$ in $G$, then $G$ has a 2-factor with exactly $k$ cycles. This is a common generalization of the results obtained by Brandt et al. [Degree conditions for 2-factors, J. Graph Theory 24 (1997) 165-173] and Yamashita [On degree sum conditions for long cycles and cycles through specified vertices, Discrete Math. 308 (2008) 6584-6587], respectively.

math.CO↗
arXiv2017

On the existence of vertex-disjoint subgraphs with high degree sum

For a graph $G$, we denote by $σ_{2}(G)$ the minimum degree sum of two non-adjacent vertices if $G$ is non-complete; otherwise, $σ_{2}(G) = +\infty$. In this paper, we prove the following two results: (i) If $s_{1}, s_{2} \ge 2$ are integers and $G$ is a non-complete graph with $σ_{2}(G) \ge 2(s_{1} + s_{2} + 1) - 1$, then $G$ contains two vertex-disjoint subgraphs $H_{1}$ and $H_{2}$ such that each $H_{i}$ is a graph of order at least $s_{i}+1$ with $σ_{2}(H_{i}) \ge 2s_{i} - 1$. (ii) If $s_{1}, s_{2} \ge 2$ are integers and $G$ is a triangle-free graph of order at least $3$ with $σ_{2}(G) \ge 2(s_{1} + s_{2}) - 1$, then $G$ contains two vertex-disjoint subgraphs $H_{1}$ and $H_{2}$ such that each $H_{i}$ is a graph of order at least $2s_{i}$ with $σ_{2}(H_{i}) \ge 2s_{i} - 1$. By using this result, we also give some corollaries concerning degree conditions for the existence of $k$ vertex-disjoint cycles.

math.CO↗
arXiv2015

Dominating cycles and forbidden pairs containing a path of order 5

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 pairs guaranteeing the existence of a dominating cycle and show the following two results: (i) Every $2$-connected $\{P_{5}, K_{4}^{-}\}$-free graph contains a longest cycle which is a dominating cycle. (ii) Every $2$-connected $\{P_{5}, W^{*}\}$-free graph contains a longest cycle which is a dominating cycle. Here $P_{5}$ is the path of order $5$, $K_{4}^{-}$ is the graph obtained from the complete graph of order $4$ by removing one edge, and $W^{*}$ is a graph obtained from two triangles and an edge by identifying one vertex in each.

math.CO↗
arXiv2015

Forbidden pairs and the existence of a dominating cycle

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 of a dominating cycle in 2-connected graphs.

math.CO↗