13 problems

Liang's conjecture. If every node in $S$ has degree at most $4$ and every node in $T$ has degree at most $3$, then $G$ has a matching $M$ and a family $\mathcal{F}$ of node-disjoin…

Let $G$ be a graph with $k$ pendant edges, let $\Delta(G)$ be its maximum degree, and let $\chi_{lt}(G)$ denote its local total antimagic chromatic number. Local total antimagic bo…

Let $T$ be a complete full $t$-ary tree, meaning a rooted tree in which every nonleaf has exactly $t$ children and all leaves have the same depth. Let $l$ be the number of leaves a…

Let $G$ be a graph with no component isomorphic to $K_2$. A local antimagic labeling is a bijection $f:E(G)\to\{1,2,\ldots,|E(G)|\}$ for which adjacent vertices have distinct verte…

Let $T$ be a tree with $l$ leaves, and let $\chi_{la}(T)$ denote its local antimagic chromatic number, the minimum number of colors induced by a local antimagic labeling. The local…

Let $G$ be a graph and let $t$ be a positive integer. Write $G\cup tP_3$ for the disjoint union of $G$ and $t$ copies of $P_3$, and let $\tau(G)$ be the maximum integer such that…

Let $G$ and $H$ be antimagic graphs, and let $G\cup H$ denote their disjoint union. For an antimagic graph $X$, define $\tau(X)$ as the maximum integer such that $X\cup tP_3$ is an…

Cycle threshold conjecture. For every $n$, $\tau(C_n)=\beta(C_n)$; equivalently, $C_n\cup tP_3$ is antimagic exactly when

Let $G$ be a spider forest, meaning a graph whose components are spiders, and let $m=|E(G)|$. A labeling $f:E(G)\to[k+1,k+m]$ is $k$-shifted antimagic if it is a bijection and the…

Let $G$ be a graph, and let $k$ be an integer. A $k$-shifted-antimagic labeling of $G$ is an injective edge labeling by the consecutive integers $k+1,k+2,\ldots,k+|E(G)|$ such that…

A linear forest is a disjoint union of paths, and a linear forest is $\\{P_2,P_3\\}$-free when none of its components is isomorphic to $P_2$ or $P_3$. An antimagic labeling assigns…

Let $G$ be a graph with $m$ edges and no isolated edge. For each vertex $v$, let $S_v$ be the sum of the labels on edges incident with $v$. A distance-two antimagic labelling uses…

Let $T$ be a tree, and let $P_2$ denote the path on two vertices. A vertex-antimagic edge (VAE) labeling of $T$ assigns distinct labels to the edges so that the sums of the labels…