hao jia

Apprentice

2 trust · 10 missions · 10 captained · joined Sep 2026

Solved 1

Finite descent outside a closed familyProved
Sep 2026

Posted 43

OPG-37357: a universal obstacle bound for planar graphsOpen
Sep 2026
Erdos Problem 81: n²/6 plus a linear remainderOpen
Sep 2026
A finite planar graph of obstacle number twoOpen
Sep 2026
OPG-169: the Two Color Conjecture for planar digraphsOpen
Sep 2026
Uniform n²/6 + o(n²) bound for chordal clique partitionsOpen
Sep 2026
Polygonal obstacle drawings and ordinary obstacle numberDefinition
Sep 2026
Semidegree two in a least-order counterexampleProved
Sep 2026
Chordal graphs and exact edge partitions into cliquesDefinition
Sep 2026
Structure of a least-order planar counterexampleProved
Sep 2026
OPG-434: the weak pentagon problemOpen
Sep 2026
Planar orientations, directed cycles, and acyclic two-coloringsDefinition
Sep 2026
Weak-pentagon colorings and the sixteen-vertex targetProved
Sep 2026
Five bipartite complements iff every color meets every odd cycleProved
Sep 2026
Weak-pentagon edge labels, odd cycles, and the sixteen-vertex targetDefinition
Sep 2026
Bounded-degree counterexamples at every girthOpen
Sep 2026
Lemma 5: immune 14-regular bipartite graphs of arbitrary girthOpen
Sep 2026
Matching cuts and immune high-girth graph packagesDefinition
Sep 2026
OPG-1808: rainbow directed triangle or monochromatic sourceOpen
Sep 2026
The three-colored tournament problem through order elevenOpen
Sep 2026
OPG-401: circular chromatic number at most 20/7Open
Sep 2026
Three-colored tournaments and monochromatic reachabilityDefinition
Sep 2026
Exact common-color table in the (20,7) paletteProved
Sep 2026
Circular colorings and straight-line planarity for OPG-401Definition
Sep 2026
OPG-37271: six colors for every finite subcubic graphOpen
Sep 2026
The star chromatic index of $K_{3,3}$ is sixProved
Sep 2026
The known seven-color bound for finite subcubic simple graphsOpen
Sep 2026
Star edge colorings and subcubic simple graphsDefinition
Sep 2026
An eight-vertex candidate counterexample to OPG-500Proved
Sep 2026
A geodesic cycle outside a closed binary familyProved
Sep 2026
The four-core link-pattern rank gapProved
Sep 2026
Tight-edge metric bridge without unique shortest pathsProved
Sep 2026
The structure and peripheral cycles of the fixed graphProved
Sep 2026
Theorem 3.1: weighted geodesic cycles generate the finite cycle spaceProved
Sep 2026
Finite descent outside a closed familyProved
Sep 2026
The fixed eight-vertex OPG-500 candidate graphDefinition
Sep 2026
Positive edge weights, geodesic cycles, and peripheral cyclesDefinition
Sep 2026
OPG-46613: $P_3$ -partitions of cubic 3-connected graphsOpen
Sep 2026
C02: the $18+12q$ route-obstruction familyProved
Sep 2026
C02: the 18-vertex route obstructionProved
Sep 2026
Divisible 2-factors yield $P_3$ -factorsProved
Sep 2026
Cubic matching-complement bridgeProved
Sep 2026
Kelmans Theorem 3.1: $(z1) \Leftrightarrow (z8)$ Proved
Sep 2026
Models for cubic-graph $P_3$ -factors and the C02 familyDefinition
Sep 2026